How do I use Homotopy Perturbation Method to find ...

Please, I need to use Maple to solve Euler-Bernoulli Beam on Pasternak Foundation using Homotopy Perturbation Method.

The governing equation is

initial conditions are

the boundary condition is

The governing equation represents Euler-Bernoulli beam on a generalized Pasternak viscoelastic foundation under an
arbitrary distributed dynamic load. in which E, I , ρ ,A are the parameters of the beam, representing Young’s modulus of elasticity, moment of inertia, density and area of cross section, respectively. K,C and Gp are spring stiffness, damping coefficient, and shear coefficient of the foundation. Moreover, y(x, t) and F(x, t) are defined as the vertical deflection of the beam and the generic arbitrary dynamic loads, respectively, where the loads distribute along the x-axis and t is time.

I will appreciate anyone who can help me with a Maple solution.

Thank you.

Unique solution using pdsolve...

Hi

I have a first oder PDE, I use pdsolve I obtained a solution depend on function F

condition_unique_solution.mw

My question: The boundary condition  f(x,y) = 1 is supplied on the line y = k x, where k is a constant. For which k
does there exist a unique solution for f(x, y)?

`System error, `, "bad id" ; what does it mean?...

Hi everybody

I try to save an array of equations in a "mpl file", and then read file and array by command read mpl file. But system error "bad id" occurs. Previously I saved this mpl file by "save" and read array by "read" command. I ran this code several times without any problem, suddenly error "bad id" occurred. When I save mpl file by the code edit region and then read it by "read" in the same or  a new worksheet, the error doesn't happen!
What is wrong?
"Id" refers to the array index?

Thanks.
Maple 18 and Windows 10

variable spacestep for numerical solution of pde...

Dear all,
How can I input different spacesteps in numerical solution of PDE (Heat equation) with pdsolve of Maple?

For example, the x range is x=0..L,
and I'd like to solve the PDE with spacestep1=L/100 for x=0..a and spacestep2=L/10 for x=a..L.

solve problem how to fix it...

restart;
T := K+F(xi)*F(xi);
2
K + F(xi)
U := alpha[0]+alpha[1]*(m+F(xi))+beta[1]/(m+F(xi))+alpha[2]*(m+F(xi))*(m+F(xi))+beta[2]/(m+F(xi))^2;
beta[1]
alpha[0] + alpha[1] (m + F(xi)) + ---------
m + F(xi)

2     beta[2]
+ alpha[2] (m + F(xi))  + ------------
2
(m + F(xi))
diff(U, xi);
/ d        \
beta[1] |---- F(xi)|
/ d        \           \ dxi      /
alpha[1] |---- F(xi)| - --------------------
\ dxi      /                  2
(m + F(xi))

/ d        \
2 beta[2] |---- F(xi)|
/ d        \             \ dxi      /
+ 2 alpha[2] (m + F(xi)) |---- F(xi)| - ----------------------
\ dxi      /                   3
(m + F(xi))
d := alpha[1]*T-beta[1]*T/(m+F(xi))^2+2*alpha[2]*(m+F(xi))*T-2*beta[2]*T/(m+F(xi))^3;
/         2\
/         2\   beta[1] \K + F(xi) /
alpha[1] \K + F(xi) / - --------------------
2
(m + F(xi))

/         2\
/         2\   2 beta[2] \K + F(xi) /
+ 2 alpha[2] (m + F(xi)) \K + F(xi) / - ----------------------
3
(m + F(xi))
diff(d, xi);
/ d        \
2 beta[1] F(xi) |---- F(xi)|
/ d        \                   \ dxi      /
2 alpha[1] F(xi) |---- F(xi)| - ----------------------------
\ dxi      /                      2
(m + F(xi))

/         2\ / d        \
2 beta[1] \K + F(xi) / |---- F(xi)|
\ dxi      /
+ -----------------------------------
3
(m + F(xi))

/ d        \ /         2\
+ 2 alpha[2] |---- F(xi)| \K + F(xi) /
\ dxi      /

/ d        \
+ 4 alpha[2] (m + F(xi)) F(xi) |---- F(xi)|
\ dxi      /

/ d        \
4 beta[2] F(xi) |---- F(xi)|
\ dxi      /
- ----------------------------
3
(m + F(xi))

/         2\ / d        \
6 beta[2] \K + F(xi) / |---- F(xi)|
\ dxi      /
+ -----------------------------------
4
(m + F(xi))
collect(%, diff);
/                                               /         2\
|                   2 beta[1] F(xi)   2 beta[1] \K + F(xi) /
|2 alpha[1] F(xi) - --------------- + ----------------------
|                               2                     3
\                    (m + F(xi))           (m + F(xi))

/         2\
+ 2 alpha[2] \K + F(xi) / + 4 alpha[2] (m + F(xi)) F(xi)

/         2\\
4 beta[2] F(xi)   6 beta[2] \K + F(xi) /| / d        \
- --------------- + ----------------------| |---- F(xi)|
3                     4     | \ dxi      /
(m + F(xi))           (m + F(xi))      /
S := (2*alpha[1]*F(xi)-2*beta[1]*F(xi)/(m+F(xi))^2+2*beta[1]*(K+F(xi)^2)/(m+F(xi))^3+2*alpha[2]*(K+F(xi)^2)+4*alpha[2]*(m+F(xi))*F(xi)-4*beta[2]*F(xi)/(m+F(xi))^3+6*beta[2]*(K+F(xi)^2)/(m+F(xi))^4)*T;
/                                               /         2\
|                   2 beta[1] F(xi)   2 beta[1] \K + F(xi) /
|2 alpha[1] F(xi) - --------------- + ----------------------
|                               2                     3
\                    (m + F(xi))           (m + F(xi))

/         2\
+ 2 alpha[2] \K + F(xi) / + 4 alpha[2] (m + F(xi)) F(xi)

/         2\\
4 beta[2] F(xi)   6 beta[2] \K + F(xi) /| /         2\
- --------------- + ----------------------| \K + F(xi) /
3                     4     |
(m + F(xi))           (m + F(xi))      /
expand((2*w*k*k)*beta*S-(2*A*k*k)*d-2*w*U+k*U*U);
2                   2               2
-2 A k  alpha[1] K - 2 A k  alpha[1] F(xi)

2               3
- 4 A k  alpha[2] F(xi)  - 4 w alpha[2] F(xi) m

+ 2 k alpha[0] alpha[1] m + 2 k alpha[0] alpha[1] F(xi)

2 k alpha[0] beta[1]                          2
+ -------------------- + 2 k alpha[0] alpha[2] m
m + F(xi)

2   2 k alpha[0] beta[2]
+ 2 k alpha[0] alpha[2] F(xi)  + --------------------
2
(m + F(xi))

2                         3
+ 2 k alpha[1]  m F(xi) + 2 k alpha[1] m  alpha[2]

3            2 k beta[1] beta[2]
+ 2 k alpha[1] F(xi)  alpha[2] + -------------------
3
(m + F(xi))

2  3                     2  2      2
+ 4 k alpha[2]  m  F(xi) + 6 k alpha[2]  m  F(xi)

2      3                              2
+ 4 k alpha[2]  F(xi)  m - 2 w alpha[0] + k alpha[0]

2                    3        2                2
+ 4 w k  beta alpha[1] F(xi)  + 4 w k  beta alpha[2] K

2
2                    4   2 A k  beta[1] K
+ 12 w k  beta alpha[2] F(xi)  + ----------------
2
(m + F(xi))

2              2
2 A k  beta[1] F(xi)         2
+ --------------------- - 4 A k  alpha[2] m K
2
(m + F(xi))

2                 2        2
- 4 A k  alpha[2] m F(xi)  - 4 A k  alpha[2] F(xi) K

2                  2              2
4 A k  beta[2] K   4 A k  beta[2] F(xi)
+ ---------------- + ---------------------
3                    3
(m + F(xi))          (m + F(xi))

2 k alpha[1] m beta[1]
+ 4 k alpha[0] alpha[2] F(xi) m + ----------------------
m + F(xi)

2
+ 6 k alpha[1] m  alpha[2] F(xi)

2   2 k alpha[1] m beta[2]
+ 6 k alpha[1] m alpha[2] F(xi)  + ----------------------
2
(m + F(xi))

2 k alpha[1] F(xi) beta[1]   2 k alpha[1] F(xi) beta[2]
+ -------------------------- + --------------------------
m + F(xi)                              2
(m + F(xi))

2                             2
2 k beta[1] alpha[2] m    2 k beta[1] alpha[2] F(xi)
+ ----------------------- + ---------------------------
m + F(xi)                   m + F(xi)

2                             2
2 k alpha[2] m  beta[2]   2 k alpha[2] F(xi)  beta[2]
+ ----------------------- + ---------------------------
2                           2
(m + F(xi))                 (m + F(xi))

2
2  2             2      2    k beta[1]
+ k alpha[1]  m  + k alpha[1]  F(xi)  + ------------
2
(m + F(xi))

2
2  4             2      4    k beta[2]
+ k alpha[2]  m  + k alpha[2]  F(xi)  + ------------
4
(m + F(xi))

2 w beta[1]
- 2 w alpha[1] m - 2 w alpha[1] F(xi) - -----------
m + F(xi)

2                     2   2 w beta[2]
- 2 w alpha[2] m  - 2 w alpha[2] F(xi)  - ------------
2
(m + F(xi))

2                             2                     2
4 w k  beta beta[1] F(xi) K   8 w k  beta beta[1] K F(xi)
- --------------------------- + ----------------------------
2                              3
(m + F(xi))                    (m + F(xi))

2
2                           8 w k  beta beta[2] F(xi) K
+ 8 w k  beta alpha[2] F(xi) m K - ---------------------------
3
(m + F(xi))

2                     2
24 w k  beta beta[2] K F(xi)         2
+ ----------------------------- + 4 w k  beta alpha[1] F(xi) K
4
(m + F(xi))

2                   3        2               2
4 w k  beta beta[1] F(xi)    4 w k  beta beta[1] K
- -------------------------- + ----------------------
2                          3
(m + F(xi))                (m + F(xi))

2                   4
4 w k  beta beta[1] F(xi)          2                      2
+ -------------------------- + 16 w k  beta alpha[2] K F(xi)
3
(m + F(xi))

2                   3
2                    3     8 w k  beta beta[2] F(xi)
+ 8 w k  beta alpha[2] F(xi)  m - --------------------------
3
(m + F(xi))

2               2         2                   4
12 w k  beta beta[2] K    12 w k  beta beta[2] F(xi)
+ ----------------------- + ---------------------------
4                           4
(m + F(xi))                 (m + F(xi))

4 k beta[1] alpha[2] F(xi) m   4 k alpha[2] F(xi) m beta[2]
+ ---------------------------- + ----------------------------
m + F(xi)                                2
(m + F(xi))
value(%);
2                   2               2
-2 A k  alpha[1] K - 2 A k  alpha[1] F(xi)

2               3
- 4 A k  alpha[2] F(xi)  - 4 w alpha[2] F(xi) m

+ 2 k alpha[0] alpha[1] m + 2 k alpha[0] alpha[1] F(xi)

2 k alpha[0] beta[1]                          2
+ -------------------- + 2 k alpha[0] alpha[2] m
m + F(xi)

2   2 k alpha[0] beta[2]
+ 2 k alpha[0] alpha[2] F(xi)  + --------------------
2
(m + F(xi))

2                         3
+ 2 k alpha[1]  m F(xi) + 2 k alpha[1] m  alpha[2]

3            2 k beta[1] beta[2]
+ 2 k alpha[1] F(xi)  alpha[2] + -------------------
3
(m + F(xi))

2  3                     2  2      2
+ 4 k alpha[2]  m  F(xi) + 6 k alpha[2]  m  F(xi)

2      3                              2
+ 4 k alpha[2]  F(xi)  m - 2 w alpha[0] + k alpha[0]

2                    3        2                2
+ 4 w k  beta alpha[1] F(xi)  + 4 w k  beta alpha[2] K

2
2                    4   2 A k  beta[1] K
+ 12 w k  beta alpha[2] F(xi)  + ----------------
2
(m + F(xi))

2              2
2 A k  beta[1] F(xi)         2
+ --------------------- - 4 A k  alpha[2] m K
2
(m + F(xi))

2                 2        2
- 4 A k  alpha[2] m F(xi)  - 4 A k  alpha[2] F(xi) K

2                  2              2
4 A k  beta[2] K   4 A k  beta[2] F(xi)
+ ---------------- + ---------------------
3                    3
(m + F(xi))          (m + F(xi))

2 k alpha[1] m beta[1]
+ 4 k alpha[0] alpha[2] F(xi) m + ----------------------
m + F(xi)

2
+ 6 k alpha[1] m  alpha[2] F(xi)

2   2 k alpha[1] m beta[2]
+ 6 k alpha[1] m alpha[2] F(xi)  + ----------------------
2
(m + F(xi))

2 k alpha[1] F(xi) beta[1]   2 k alpha[1] F(xi) beta[2]
+ -------------------------- + --------------------------
m + F(xi)                              2
(m + F(xi))

2                             2
2 k beta[1] alpha[2] m    2 k beta[1] alpha[2] F(xi)
+ ----------------------- + ---------------------------
m + F(xi)                   m + F(xi)

2                             2
2 k alpha[2] m  beta[2]   2 k alpha[2] F(xi)  beta[2]
+ ----------------------- + ---------------------------
2                           2
(m + F(xi))                 (m + F(xi))

2
2  2             2      2    k beta[1]
+ k alpha[1]  m  + k alpha[1]  F(xi)  + ------------
2
(m + F(xi))

2
2  4             2      4    k beta[2]
+ k alpha[2]  m  + k alpha[2]  F(xi)  + ------------
4
(m + F(xi))

2 w beta[1]
- 2 w alpha[1] m - 2 w alpha[1] F(xi) - -----------
m + F(xi)

2                     2   2 w beta[2]
- 2 w alpha[2] m  - 2 w alpha[2] F(xi)  - ------------
2
(m + F(xi))

2                             2                     2
4 w k  beta beta[1] F(xi) K   8 w k  beta beta[1] K F(xi)
- --------------------------- + ----------------------------
2                              3
(m + F(xi))                    (m + F(xi))

2
2                           8 w k  beta beta[2] F(xi) K
+ 8 w k  beta alpha[2] F(xi) m K - ---------------------------
3
(m + F(xi))

2                     2
24 w k  beta beta[2] K F(xi)         2
+ ----------------------------- + 4 w k  beta alpha[1] F(xi) K
4
(m + F(xi))

2                   3        2               2
4 w k  beta beta[1] F(xi)    4 w k  beta beta[1] K
- -------------------------- + ----------------------
2                          3
(m + F(xi))                (m + F(xi))

2                   4
4 w k  beta beta[1] F(xi)          2                      2
+ -------------------------- + 16 w k  beta alpha[2] K F(xi)
3
(m + F(xi))

2                   3
2                    3     8 w k  beta beta[2] F(xi)
+ 8 w k  beta alpha[2] F(xi)  m - --------------------------
3
(m + F(xi))

2               2         2                   4
12 w k  beta beta[2] K    12 w k  beta beta[2] F(xi)
+ ----------------------- + ---------------------------
4                           4
(m + F(xi))                 (m + F(xi))

4 k beta[1] alpha[2] F(xi) m   4 k alpha[2] F(xi) m beta[2]
+ ---------------------------- + ----------------------------
m + F(xi)                                2
(m + F(xi))

expr := simplify(%);
2                   2               2
-2 A k  alpha[1] K - 2 A k  alpha[1] F(xi)

2               3
- 4 A k  alpha[2] F(xi)  - 4 w alpha[2] F(xi) m

+ 2 k alpha[0] alpha[1] m + 2 k alpha[0] alpha[1] F(xi)

2 k alpha[0] beta[1]                          2
+ -------------------- + 2 k alpha[0] alpha[2] m
m + F(xi)

2   2 k alpha[0] beta[2]
+ 2 k alpha[0] alpha[2] F(xi)  + --------------------
2
(m + F(xi))

2                         3
+ 2 k alpha[1]  m F(xi) + 2 k alpha[1] m  alpha[2]

3            2 k beta[1] beta[2]
+ 2 k alpha[1] F(xi)  alpha[2] + -------------------
3
(m + F(xi))

2  3                     2  2      2
+ 4 k alpha[2]  m  F(xi) + 6 k alpha[2]  m  F(xi)

2      3                              2
+ 4 k alpha[2]  F(xi)  m - 2 w alpha[0] + k alpha[0]

2                    3        2                2
+ 4 w k  beta alpha[1] F(xi)  + 4 w k  beta alpha[2] K

2
2                    4   2 A k  beta[1] K
+ 12 w k  beta alpha[2] F(xi)  + ----------------
2
(m + F(xi))

2              2
2 A k  beta[1] F(xi)         2
+ --------------------- - 4 A k  alpha[2] m K
2
(m + F(xi))

2                 2        2
- 4 A k  alpha[2] m F(xi)  - 4 A k  alpha[2] F(xi) K

2                  2              2
4 A k  beta[2] K   4 A k  beta[2] F(xi)
+ ---------------- + ---------------------
3                    3
(m + F(xi))          (m + F(xi))

2 k alpha[1] m beta[1]
+ 4 k alpha[0] alpha[2] F(xi) m + ----------------------
m + F(xi)

2
+ 6 k alpha[1] m  alpha[2] F(xi)

2   2 k alpha[1] m beta[2]
+ 6 k alpha[1] m alpha[2] F(xi)  + ----------------------
2
(m + F(xi))

2 k alpha[1] F(xi) beta[1]   2 k alpha[1] F(xi) beta[2]
+ -------------------------- + --------------------------
m + F(xi)                              2
(m + F(xi))

2                             2
2 k beta[1] alpha[2] m    2 k beta[1] alpha[2] F(xi)
+ ----------------------- + ---------------------------
m + F(xi)                   m + F(xi)

2                             2
2 k alpha[2] m  beta[2]   2 k alpha[2] F(xi)  beta[2]
+ ----------------------- + ---------------------------
2                           2
(m + F(xi))                 (m + F(xi))

2
2  2             2      2    k beta[1]
+ k alpha[1]  m  + k alpha[1]  F(xi)  + ------------
2
(m + F(xi))

2
2  4             2      4    k beta[2]
+ k alpha[2]  m  + k alpha[2]  F(xi)  + ------------
4
(m + F(xi))

2 w beta[1]
- 2 w alpha[1] m - 2 w alpha[1] F(xi) - -----------
m + F(xi)

2                     2   2 w beta[2]
- 2 w alpha[2] m  - 2 w alpha[2] F(xi)  - ------------
2
(m + F(xi))

2                             2                     2
4 w k  beta beta[1] F(xi) K   8 w k  beta beta[1] K F(xi)
- --------------------------- + ----------------------------
2                              3
(m + F(xi))                    (m + F(xi))

2
2                           8 w k  beta beta[2] F(xi) K
+ 8 w k  beta alpha[2] F(xi) m K - ---------------------------
3
(m + F(xi))

2                     2
24 w k  beta beta[2] K F(xi)         2
+ ----------------------------- + 4 w k  beta alpha[1] F(xi) K
4
(m + F(xi))

2                   3        2               2
4 w k  beta beta[1] F(xi)    4 w k  beta beta[1] K
- -------------------------- + ----------------------
2                          3
(m + F(xi))                (m + F(xi))

2                   4
4 w k  beta beta[1] F(xi)          2                      2
+ -------------------------- + 16 w k  beta alpha[2] K F(xi)
3
(m + F(xi))

2                   3
2                    3     8 w k  beta beta[2] F(xi)
+ 8 w k  beta alpha[2] F(xi)  m - --------------------------
3
(m + F(xi))

2               2         2                   4
12 w k  beta beta[2] K    12 w k  beta beta[2] F(xi)
+ ----------------------- + ---------------------------
4                           4
(m + F(xi))                 (m + F(xi))

4 k beta[1] alpha[2] F(xi) m   4 k alpha[2] F(xi) m beta[2]
+ ---------------------------- + ----------------------------
m + F(xi)                                2
(m + F(xi))

temp := algsubs(m+F(xi) = freeze(m+F(xi)), numer(expr));
/        2            4                    2
\4 beta k  w freeze/R0  alpha[2] + 4 beta k  w freeze/R0 beta[1]

2          \      4   /        2            5
+ 12 beta k  w beta[2]/ F(xi)  + \8 beta k  w freeze/R0  alpha

2            4
[2] + 4 beta k  w freeze/R0  alpha[1]

2            2
- 4 beta k  w freeze/R0  beta[1]

2                    \      3   /          2
- 8 beta k  w freeze/R0 beta[2]/ F(xi)  + \8 K beta k  w

4                 2          5
freeze/R0  alpha[2] - 4 A k  freeze/R0  alpha[2]

2          4                 2          2
- 2 A k  freeze/R0  alpha[1] + 2 A k  freeze/R0  beta[1]

2                                  2
+ 8 w k  beta beta[1] K freeze/R0 + 24 w k  beta beta[2] K

2                  \      2   /          2            5
+ 4 A k  beta[2] freeze/R0/ F(xi)  + \8 K beta k  w freeze/R0

2            4
alpha[2] + 4 K beta k  w freeze/R0  alpha[1]

2            2
- 4 K beta k  w freeze/R0  beta[1]

2                    \
- 8 K beta k  w freeze/R0 beta[2]/ F(xi)

2          8              6         2
+ k alpha[2]  freeze/R0  + k freeze/R0  alpha[1]

6                         5
- 2 w freeze/R0  alpha[2] - 2 w freeze/R0  alpha[1]

4           2              4
+ freeze/R0  k alpha[0]  - 2 freeze/R0  w alpha[0]

7
+ 2 k alpha[1] alpha[2] freeze/R0

6
+ 2 k freeze/R0  alpha[0] alpha[2]

5
+ 2 k freeze/R0  alpha[0] alpha[1]

5
+ 2 k freeze/R0  alpha[2] beta[1]

4
+ 2 freeze/R0  k alpha[1] beta[1]

4
+ 2 freeze/R0  k alpha[2] beta[2]

3
+ 2 k freeze/R0  alpha[0] beta[1]

3
+ 2 k freeze/R0  alpha[1] beta[2]

2
+ 2 k freeze/R0  alpha[0] beta[2]

2          5                       4    2
- 4 A K k  freeze/R0  alpha[2] - 2 freeze/R0  A k  alpha[1] K

2          2
+ 2 A K k  freeze/R0  beta[1]

4    2                2
+ 4 freeze/R0  w k  beta alpha[2] K

2               2                          3
+ 4 w k  beta beta[1] K  freeze/R0 - 2 w freeze/R0  beta[1]

2        2                2
+ k freeze/R0  beta[1]  - 2 w freeze/R0  beta[2]

2
+ 4 A k  beta[2] K freeze/R0 + 2 k beta[1] beta[2] freeze/R0

2         2               2
+ k beta[2]  + 12 w k  beta beta[2] K
thaw(collect(temp, freeze(m+F(xi)))/denom(expr));
1       /          2            8
------------ \k alpha[2]  (m + F(xi))
4
(m + F(xi))

7              6 /
+ 2 k alpha[1] alpha[2] (m + F(xi))  + (m + F(xi))  \2 k alpha

2               \   /       3       2
[0] alpha[2] + k alpha[1]  - 2 w alpha[2]/ + \8 F(xi)  beta k  w

2
alpha[2] + 8 K F(xi) beta k  w alpha[2]

2  2                   2
- 4 A F(xi)  k  alpha[2] - 4 A K k  alpha[2]

\
+ 2 k alpha[0] alpha[1] + 2 k alpha[2] beta[1] - 2 w alpha[1]/

5   /     2                    4
(m + F(xi))  + \4 w k  beta alpha[2] F(xi)

2                    3
+ 4 w k  beta alpha[1] F(xi)

/          2                   2         \      2
+ \8 K beta k  w alpha[2] - 2 A k  alpha[1]/ F(xi)

2                                   2
+ 4 w k  beta alpha[1] F(xi) K + k alpha[0]  - 2 w alpha[0]

+ 2 k alpha[1] beta[1] + 2 k alpha[2] beta[2]

2                   2                2\            4
- 2 A k  alpha[1] K + 4 w k  beta alpha[2] K / (m + F(xi))  +

(2 k alpha[0] beta[1] + 2 k alpha[1] beta[2] - 2 w beta[1])

3   /      2                   3
(m + F(xi))  + \-4 w k  beta beta[1] F(xi)

2                             2              2
- 4 w k  beta beta[1] F(xi) K + 2 A k  beta[1] F(xi)

2                                             2
+ 2 A k  beta[1] K + 2 k alpha[0] beta[2] + k beta[1]

\            2   /     2                   4
- 2 w beta[2]/ (m + F(xi))  + \4 w k  beta beta[1] F(xi)

2                   3
- 8 w k  beta beta[2] F(xi)

/          2                  2        \      2
+ \8 K beta k  w beta[1] + 4 A k  beta[2]/ F(xi)

2                             2               2
- 8 w k  beta beta[2] F(xi) K + 4 w k  beta beta[1] K

2                                \
+ 4 A k  beta[2] K + 2 k beta[1] beta[2]/ (m + F(xi))

2                   4         2                     2
+ 12 w k  beta beta[2] F(xi)  + 24 w k  beta beta[2] K F(xi)

2               2            2\
+ 12 w k  beta beta[2] K  + k beta[2] /
collect(%, F(xi));
1       //         2                        2\      8   /
------------ \\12 beta k  w alpha[2] + k alpha[2] / F(xi)  + \56
4
(m + F(xi))

2                        2                   2
beta k  m w alpha[2] + 4 beta k  w alpha[1] - 4 A k  alpha[2]

2                        \      7   /
+ 8 k m alpha[2]  + 2 k alpha[1] alpha[2]/ F(xi)  + \104 beta

2  2                         2
k  m  w alpha[2] + 16 K beta k  w alpha[2]

2                      2
+ 16 beta k  m w alpha[1] - 20 A k  m alpha[2]

2         2        2
+ 28 k m  alpha[2]  - 2 A k  alpha[1]

+ 14 k m alpha[1] alpha[2] + 2 k alpha[0] alpha[2]

2               \      6   /             2  3
+ k alpha[1]  - 2 w alpha[2]/ F(xi)  + \56 k alpha[2]  m

2
+ 42 k alpha[1] alpha[2] m

/                                  2               \
+ 6 m \2 k alpha[0] alpha[2] + k alpha[1]  - 2 w alpha[2]/

2                3         2
+ 96 w k  beta alpha[2] m  + 40 w k  beta alpha[2] K m

2           2          2
- 40 A k  alpha[2] m  - 4 A K k  alpha[2]

+ 2 k alpha[0] alpha[1] + 2 k alpha[2] beta[1] - 2 w alpha[1]

2
+ 4 w k  beta alpha[1] K

/          2                   2         \
+ 4 \8 K beta k  w alpha[2] - 2 A k  alpha[1]/ m

2                2\      5   /             2  4
+ 24 w k  beta alpha[1] m / F(xi)  + \70 k alpha[2]  m

3
+ 70 k alpha[1] m  alpha[2]

2 /                                  2               \
+ 15 m  \2 k alpha[0] alpha[2] + k alpha[1]  - 2 w alpha[2]/ + 5

/        2
\-4 A K k  alpha[2] + 2 k alpha[0] alpha[1]

\
+ 2 k alpha[2] beta[1] - 2 w alpha[1]/ m

2                  2         2           3
+ 80 w k  beta alpha[2] K m  - 40 A k  alpha[2] m

2                4        2                2
+ 44 w k  beta alpha[2] m  + 4 w k  beta alpha[2] K

2                        2
- 2 A k  alpha[1] K + k alpha[0]  + 2 k alpha[1] beta[1]

+ 2 k alpha[2] beta[2] - 2 w alpha[0]

2
+ 16 w k  beta alpha[1] K m

/          2                   2         \  2
+ 6 \8 K beta k  w alpha[2] - 2 A k  alpha[1]/ m

2                3        2
+ 16 w k  beta alpha[1] m  - 4 w k  beta beta[1] m

2                2             \      4   /
+ 2 A k  beta[1] + 4 w k  beta beta[2]/ F(xi)  + \56 k

2  5                           4
alpha[2]  m  + 70 k alpha[1] alpha[2] m

3 /                                  2               \
+ 20 m  \2 k alpha[0] alpha[2] + k alpha[1]  - 2 w alpha[2]/ + 10

/        2
\-4 A K k  alpha[2] + 2 k alpha[0] alpha[1]

\  2
+ 2 k alpha[2] beta[1] - 2 w alpha[1]/ m

2                  3         2           4
+ 80 w k  beta alpha[2] K m  - 20 A k  alpha[2] m

2                5     /   2       2
+ 8 w k  beta alpha[2] m  + 4 \4 K  beta k  w alpha[2]

2                      2
- 2 A K k  alpha[1] + k alpha[0]  + 2 k alpha[1] beta[1]

\
+ 2 k alpha[2] beta[2] - 2 w alpha[0]/ m

2                  2
+ 24 w k  beta alpha[1] K m

/          2                   2         \  3
+ 4 \8 K beta k  w alpha[2] - 2 A k  alpha[1]/ m

2                4
+ 4 w k  beta alpha[1] m  + 2 k alpha[0] beta[1]

2               2
+ 2 k alpha[1] beta[2] - 2 w beta[1] - 4 w k  beta beta[1] m

2                       2
+ 4 w k  beta beta[1] K + 4 A k  beta[1] m

2                       2        \      3   /
- 8 w k  beta beta[2] m + 4 A k  beta[2]/ F(xi)  + \28 k

2  6                           5
alpha[2]  m  + 42 k alpha[1] alpha[2] m

4 /                                  2               \
+ 15 m  \2 k alpha[0] alpha[2] + k alpha[1]  - 2 w alpha[2]/ + 10

/        2
\-4 A K k  alpha[2] + 2 k alpha[0] alpha[1]

\  3
+ 2 k alpha[2] beta[1] - 2 w alpha[1]/ m

2                  4        2           5     /   2
+ 40 w k  beta alpha[2] K m  - 4 A k  alpha[2] m  + 6 \4 K

2                     2                      2
beta k  w alpha[2] - 2 A K k  alpha[1] + k alpha[0]

\
+ 2 k alpha[1] beta[1] + 2 k alpha[2] beta[2] - 2 w alpha[0]/

2         2                  3
m  + 16 w k  beta alpha[1] K m

/          2                   2         \  4
+ \8 K beta k  w alpha[2] - 2 A k  alpha[1]/ m

+ 3 (2 k alpha[0] beta[1] + 2 k alpha[1] beta[2] - 2 w beta[1]

2                         2          2
) m - 8 w k  beta beta[1] K m + 2 A k  beta[1] m

2                                             2
+ 2 A k  beta[1] K + 2 k alpha[0] beta[2] + k beta[1]

2
- 2 w beta[2] + 16 w k  beta beta[2] K

/          2                  2        \  \      2   /
+ \8 K beta k  w beta[1] + 4 A k  beta[2]/ m/ F(xi)  + \8 k

2  7                           6
alpha[2]  m  + 14 k alpha[1] alpha[2] m

5 /                                  2               \
+ 6 m  \2 k alpha[0] alpha[2] + k alpha[1]  - 2 w alpha[2]/ + 5

/        2
\-4 A K k  alpha[2] + 2 k alpha[0] alpha[1]

\  4
+ 2 k alpha[2] beta[1] - 2 w alpha[1]/ m

2                  5     /   2       2
+ 8 w k  beta alpha[2] K m  + 4 \4 K  beta k  w alpha[2]

2                      2
- 2 A K k  alpha[1] + k alpha[0]  + 2 k alpha[1] beta[1]

\  3
+ 2 k alpha[2] beta[2] - 2 w alpha[0]/ m

2                  4
+ 4 w k  beta alpha[1] K m

+ 3 (2 k alpha[0] beta[1] + 2 k alpha[1] beta[2] - 2 w beta[1]

2     /       2                                           2
) m  + 2 \2 A K k  beta[1] + 2 k alpha[0] beta[2] + k beta[1]

\          2                 2
- 2 w beta[2]/ m - 4 w k  beta beta[1] K m

2               2        2
+ 4 w k  beta beta[1] K  - 8 w k  beta beta[2] K m

2                                \
+ 4 A k  beta[2] K + 2 k beta[1] beta[2]/ F(xi)

8         2        7
+ k m  alpha[2]  + 2 k m  alpha[1] alpha[2]

6 /                                  2               \   /
+ m  \2 k alpha[0] alpha[2] + k alpha[1]  - 2 w alpha[2]/ + \
2
-4 A K k  alpha[2] + 2 k alpha[0] alpha[1] + 2 k alpha[2] beta[1]

\  5   /   2       2
- 2 w alpha[1]/ m  + \4 K  beta k  w alpha[2]

2                      2
- 2 A K k  alpha[1] + k alpha[0]  + 2 k alpha[1] beta[1]

\  4
+ 2 k alpha[2] beta[2] - 2 w alpha[0]/ m

+ (2 k alpha[0] beta[1] + 2 k alpha[1] beta[2] - 2 w beta[1])

3   /       2                                           2
m  + \2 A K k  beta[1] + 2 k alpha[0] beta[2] + k beta[1]

\  2   /   2       2                    2
- 2 w beta[2]/ m  + \4 K  beta k  w beta[1] + 4 A K k  beta[2]

\           2               2
+ 2 k beta[1] beta[2]/ m + 12 w k  beta beta[2] K

2\
+ k beta[2] /
solve({k*m^8*alpha[2]^2+2*k*m^7*alpha[1]*alpha[2]+m^6*(2*k*alpha[0]*alpha[2]+k*alpha[1]^2-2*w*alpha[2])+(-4*A*K*k^2*alpha[2]+2*k*alpha[0]*alpha[1]+2*k*alpha[2]*beta[1]-2*w*alpha[1])*m^5+(4*K^2*beta*k^2*w*alpha[2]-2*A*K*k^2*alpha[1]+k*alpha[0]^2+2*k*alpha[1]*beta[1]+2*k*alpha[2]*beta[2]-2*w*alpha[0])*m^4+(2*k*alpha[0]*beta[1]+2*k*alpha[1]*beta[2]-2*w*beta[1])*m^3+(2*A*K*k^2*beta[1]+2*k*alpha[0]*beta[2]+k*beta[1]^2-2*w*beta[2])*m^2+(4*K^2*beta*k^2*w*beta[1]+4*A*K*k^2*beta[2]+2*k*beta[1]*beta[2])*m+12*w*k^2*beta*beta[2]*K^2+k*beta[2]^2 = 0, 56*k*alpha[2]^2*m^3+42*k*alpha[1]*alpha[2]*m^2+6*m*(2*k*alpha[0]*alpha[2]+k*alpha[1]^2-2*w*alpha[2])+96*w*k^2*beta*alpha[2]*m^3+40*w*k^2*beta*alpha[2]*K*m-40*A*k^2*alpha[2]*m^2-4*A*K*k^2*alpha[2]+2*k*alpha[0]*alpha[1]+2*k*alpha[2]*beta[1]-2*w*alpha[1]+4*w*k^2*beta*alpha[1]*K+(4*(8*K*beta*k^2*w*alpha[2]-2*A*k^2*alpha[1]))*m+24*w*k^2*beta*alpha[1]*m^2 = 0, 8*k*alpha[2]^2*m^7+14*k*alpha[1]*alpha[2]*m^6+6*m^5*(2*k*alpha[0]*alpha[2]+k*alpha[1]^2-2*w*alpha[2])+(5*(-4*A*K*k^2*alpha[2]+2*k*alpha[0]*alpha[1]+2*k*alpha[2]*beta[1]-2*w*alpha[1]))*m^4+8*w*k^2*beta*alpha[2]*K*m^5+(4*(4*K^2*beta*k^2*w*alpha[2]-2*A*K*k^2*alpha[1]+k*alpha[0]^2+2*k*alpha[1]*beta[1]+2*k*alpha[2]*beta[2]-2*w*alpha[0]))*m^3+4*w*k^2*beta*alpha[1]*K*m^4+(3*(2*k*alpha[0]*beta[1]+2*k*alpha[1]*beta[2]-2*w*beta[1]))*m^2+(2*(2*A*K*k^2*beta[1]+2*k*alpha[0]*beta[2]+k*beta[1]^2-2*w*beta[2]))*m-4*w*k^2*beta*beta[1]*K*m^2+4*K^2*beta*k^2*w*beta[1]-8*w*k^2*beta*beta[2]*K*m+4*A*K*k^2*beta[2]+2*k*beta[1]*beta[2] = 0, 28*k*alpha[2]^2*m^6+42*k*alpha[1]*alpha[2]*m^5+15*m^4*(2*k*alpha[0]*alpha[2]+k*alpha[1]^2-2*w*alpha[2])+(10*(-4*A*K*k^2*alpha[2]+2*k*alpha[0]*alpha[1]+2*k*alpha[2]*beta[1]-2*w*alpha[1]))*m^3+40*w*k^2*beta*alpha[2]*K*m^4-4*A*k^2*alpha[2]*m^5+(6*(4*K^2*beta*k^2*w*alpha[2]-2*A*K*k^2*alpha[1]+k*alpha[0]^2+2*k*alpha[1]*beta[1]+2*k*alpha[2]*beta[2]-2*w*alpha[0]))*m^2+16*w*k^2*beta*alpha[1]*K*m^3+(8*K*beta*k^2*w*alpha[2]-2*A*k^2*alpha[1])*m^4+(3*(2*k*alpha[0]*beta[1]+2*k*alpha[1]*beta[2]-2*w*beta[1]))*m-8*w*k^2*beta*beta[1]*K*m+2*A*k^2*beta[1]*m^2+2*A*K*k^2*beta[1]+2*k*alpha[0]*beta[2]+k*beta[1]^2-2*w*beta[2]+16*w*k^2*beta*beta[2]*K+(8*K*beta*k^2*w*beta[1]+4*A*k^2*beta[2])*m = 0, 56*k*alpha[2]^2*m^5+70*k*alpha[1]*alpha[2]*m^4+20*m^3*(2*k*alpha[0]*alpha[2]+k*alpha[1]^2-2*w*alpha[2])+(10*(-4*A*K*k^2*alpha[2]+2*k*alpha[0]*alpha[1]+2*k*alpha[2]*beta[1]-2*w*alpha[1]))*m^2+80*w*k^2*beta*alpha[2]*K*m^3-20*A*k^2*alpha[2]*m^4+8*w*k^2*beta*alpha[2]*m^5+(4*(4*K^2*beta*k^2*w*alpha[2]-2*A*K*k^2*alpha[1]+k*alpha[0]^2+2*k*alpha[1]*beta[1]+2*k*alpha[2]*beta[2]-2*w*alpha[0]))*m+24*w*k^2*beta*alpha[1]*K*m^2+(4*(8*K*beta*k^2*w*alpha[2]-2*A*k^2*alpha[1]))*m^3+4*w*k^2*beta*alpha[1]*m^4+2*k*alpha[0]*beta[1]+2*k*alpha[1]*beta[2]-2*w*beta[1]-4*w*k^2*beta*beta[1]*m^2+4*K*beta*k^2*w*beta[1]+4*A*k^2*beta[1]*m-8*w*k^2*beta*beta[2]*m+4*A*k^2*beta[2] = 0, (0*k)*alpha[2]^2*m^4+70*k*alpha[1]*m^3*alpha[2]+15*m^2*(2*k*alpha[0]*alpha[2]+k*alpha[1]^2-2*w*alpha[2])+(5*(-4*A*K*k^2*alpha[2]+2*k*alpha[0]*alpha[1]+2*k*alpha[2]*beta[1]-2*w*alpha[1]))*m+80*w*k^2*beta*alpha[2]*K*m^2-40*A*k^2*alpha[2]*m^3+44*w*k^2*beta*alpha[2]*m^4+4*K^2*beta*k^2*w*alpha[2]-2*A*K*k^2*alpha[1]+k*alpha[0]^2+2*k*alpha[1]*beta[1]+2*k*alpha[2]*beta[2]-2*w*alpha[0]+16*w*k^2*beta*alpha[1]*K*m+(6*(8*K*beta*k^2*w*alpha[2]-2*A*k^2*alpha[1]))*m^2+16*w*k^2*beta*alpha[1]*m^3-4*w*k^2*beta*beta[1]*m+2*A*k^2*beta[1]+4*w*k^2*beta*beta[2] = 0, 12*beta*k^2*w*alpha[2]+k*alpha[2]^2 = 0, 56*beta*k^2*m*w*alpha[2]+4*beta*k^2*w*alpha[1]-4*A*k^2*alpha[2]+8*k*m*alpha[2]^2+2*k*alpha[1]*alpha[2] = 0, 104*beta*k^2*m^2*w*alpha[2]+16*K*beta*k^2*w*alpha[2]+16*beta*k^2*m*w*alpha[1]-20*A*k^2*m*alpha[2]+28*k*m^2*alpha[2]^2-2*A*k^2*alpha[1]+14*k*m*alpha[1]*alpha[2]+2*k*alpha[0]*alpha[2]+k*alpha[1]^2-2*w*alpha[2] = 0}, {k, m, w, alpha[0], alpha[1], alpha[2], beta[1], beta[2]});

diff eqs with integral cofficients...

general_solution.mwI want to calculate the diff equations numerical solutions at z=500 with calling the integrals with limits -500..Z and i want the datefile of resualts

How to write an equation without compiling?...

I computed A and B matrices, now I want to write it in state space reperentation.

where

So I calculated and got this:

where but the formation is not anymore. How can I enforce Maple to output the result in the form of ?

EXCEPTION_ACCESS_VIOLATION (0xc0000005)...

Hello.

I have this problem when executing the entire worksheet or selected groups.
Also Maple can crash by itself, to its heart's content)
What I can do to solve this problem?
OS: W7 x64, Java is up to date

Thx.

HTTP Get and trying to get ImportMatrix to work wi...

I using Maple 18 (not Maple 2018) and I'm trying to figure out how to grab earthquake data from earthquakescanada database from here http://www.earthquakescanada.nrcan.gc.ca//stndon/NEDB-BNDS/bull-en.php using the HTTP requests.

First I used the default search within the web browser, and get a new address which I enter as the URL

It takes a long time to download the information and would require HTML surgery but changing the option for output to txt or csv, it's faster and in a much more readable form.  However it's not in a table or Array format, it has become a string.

Is there any way to use ImportMatrix, or ImportData to get a better format of the information?  - both give errors in Maple18.  Or am I stuck trying to use string surgery in Maple 18?  The Import command isn't available until Maple 2016 (I don't mean the Import command within ExcelTools) and I believe that works in Maple 2018 however I'm at a loss for trying to use it in Maple 18.

Very urgent!!I was try to use the command "expand"...

Just like the title described, I have encountered an error when I use the command "expand". Actually, I just follow the example, but it doesn't work. Please help me or tell me how can I solve it in other commands.

```
restart;
alias(epsilon = e, omega = w, omega[0] = w0, t[1] = t1, t[2] = t2); e := proc (t1, t2) options operator, arrow; e end proc; w0 := proc (t1, t2) options operator, arrow; w0 end proc; a := proc (t1, t2) options operator, arrow; a end proc; f := proc (t1, t2) options operator, arrow; f end proc; mu := proc (t1, t2) options operator, arrow; mu end proc;
ode := (D@@2)(u)+2*mu*e*D(u)+w0^2*u+e*w0^2*u^3-e*f*cos(omega*t) = 0;
2
@@(D, 2)(u) + 2 mu epsilon D(u) + omega[0]  u

2  3
+ epsilon omega[0]  u  - epsilon f cos(omega t) = 0
e_oredr := 1;
ode := simplify(subs(D = sum('e^(i-1)*D[i]', 'i' = 1 .. e_oredr+1), ode), {e^(e_oredr+1) = 0});
/ 3         2
\u  omega[0]  + 2 (epsilon D[2] + D[1])(u) mu - cos(omega t) f

\                   2
+ 2 D[1, 2](u)/ epsilon + omega[0]  u + D[1, 1](u) = 0
simplify(collect(%, e), {e^(e_oredr+1) = 0});

u := sum('v[i]*e^i', 'i' = 0 .. e_oredr);
epsilon v[1] + v[0]
ode := simplify(collect(ode, e), {e^2 = 0});
for i from 0 to e_oredr do eq[i] := coeff(lhs(ode), e, i) = 0 end do;
2
omega[0]  v[0] + D[1, 1](v[0]) = 0
3         2           2
v[0]  omega[0]  + omega[0]  v[1] + 2 D[1](v[0]) mu

- cos(omega t) f + 2 D[1, 2](v[0]) + D[1, 1](v[1]) = 0
remove(has, lhs(eq[1]), cos); convert(%(t1, t2), diff);
eq[1] := %-convert(f*cos(sigma*t2+t1*w0), 'exp');

v[0] := A(t2)*cos(w0*t1+B(t2)); convert(%, 'exp'); v[0] := unapply(%, t1, t2);
/1
(t1, t2) -> A(t2) |- exp(I (omega[0] t1 + B(t2)))
\2

1                              \
+ - exp(-I (omega[0] t1 + B(t2)))|
2                              /

expand(eq[1]);
Error, (in property/ConvertProperty) invalid input: PropRange uses a 2nd argument, b, which is missing
collect(%, exp(I*w0*t1));
Error, (in collect) invalid 1st argument proc (t1, t2) options operator, arrow; A(t2)*((1/2)*exp(I*(w0*t1+B(t2)))+(1/2)*exp(-I*(w0*t1+B(t2)))) end proc
coeff(%, exp(I*w0*t1));
map(proc (x) options operator, arrow; x*exp(-I*B(t2)) end proc, %);
combine(%, 'exp');
subs(I*B(t2) = I*sigma*t2-I*C(t2), B(t2) = sigma*t2-C(t2), %);
conds := combine(%, 'exp');
0
```

how to get skin friction coefficient value Cf/Re^1...

how to find skin friction value below code

restart

PDEtools[declare]((U, W, T, C)(y), prime = y):

R1 := .1; R0 := .1; m := .1; a := .1; Ha := .1; Nt := .1; Nb := .1; Pr := 6.2; Le := .6; Bi := 1; Ec := .1; k := 1; r := .1; A := 1;

sys := diff(U(y), `\$`(y, 2))+(R1*(diff(U(y), y))-2*R0*W(y))*exp(a*T(y))-a*(diff(U(y), y))*(diff(T(y), y))-Ha = 0, diff(W(y), `\$`(y, 2))+(R1*(diff(W(y), y))+2*R0*U(y))*exp(a*T(y))-a*(diff(W(y), y)) = 0, diff(T(y), `\$`(y, 2))+R1*Pr*(diff(T(y), y))+Pr*Ec*exp(-a*T(y))*((diff(U(y), y))*(diff(U(y), y))+(diff(W(y), y))*(diff(W(y), y)))+Pr*Ha*Ec*((U(y)+m*W(y))*(U(y)+m*W(y))+(W(y)-m*U(y))*(W(y)-m*U(y)))/(m^2+1)^2+Nb*(diff(T(y), y))*(diff(C(y), y))+Nt*(diff(T(y), y))*(diff(T(y), y)) = 0, diff(C(y), `\$`(y, 2))+Pr*Le*R1*(diff(C(y), y))+Nt*(diff(C(y), `\$`(y, 2)))/Nb = 0:

ba := {sys, C(0) = 0, C(1) = 1, T(1) = 0, U(0) = 0, U(1) = 0, W(0) = 0, W(1) = 0, (D(T))(0) = Bi*(T(0)-1)}:

r1 := dsolve(ba, numeric, output = Array([0., 0.5e-1, .10, .15, .20, .25, .30, .35, .40, .45, .50, .55, .60, .65, .70, .75, .80, .85, .90, .95, 1.00])):

with(plots);

p1u := odeplot(r1, [y, U(y)], 0 .. 1, numpoints = 100, labels = ["y", "U"], style = line, color = green);

plots[display]({p1u})

How to find the condition on variables such that t...

Hi all,

I have the following expression,

where K and K_P are the controller gains, k is the stiffness, b is the damper, m1 and m2 are masses.

How can I find the condition on variables such that the numerator of this expression is greater that zero?

The conditions should appear as inequalities.

 (1)

How to convert maple file into pdf file?...

How to convert maple file into the pdf file?For example the attacahed file is maple file.I want to convert this to a pdf file.

conservation_of_wave_eq.mw

I have problem with the code....

Hi, i want to investigate  chaos for the problem , cantilever beam under random narro band excitation, but the code has errors .the code is this:

restart:with(plots):      h:=1: Omega:=(0..376):alpha1:=617.2:alpha2:=1.02*10^(8): c:=.002:k:=18.4:  step:=0.1:imax:=376:  for i from 0 to imax do;  Omega[i]:=i*step:   f:=evalf(solve({((-a*Omega[i]^(2)+alpha1*a+3/(4)*alpha2*a^(3)+1/(4)*k*Omega[i]^(2)*a^(3)-(3)/(4)*k*Omega[i]^(2)*a^(3))^(2)+(c*Omega[i]*a^())^(2))=h^(2),a>0}));  ff[i]:=((rhs(f[1]))^(2))/(2):  end do:   l1:=[[Omega[n],ff[n]] \$n=0..imax]:  p1:=plot(l1, x=0..3,y=0..1,  style=point,symbol=solidcircle,symbolsize=4,color=red):    jmax:=914: f1:=array(377..914):f2:=array(377..914):f3:=array(377..914):Omega1:=array(377..914):  for j from 377to jmax do;  Omega1[j]:=j*step:   fff:=evalf(solve({((-a*Omega1[j]^(2)+alpha1*a+3/(4)*alpha2*a^(3)+1/(4)*k*Omega1[j]^(2)*a^(3)-(3)/(4)*k*Omega1[j]^(2)*a^(3))^(2)+(c*Omega1[j]*a^())^(2))=h^(2),a>0}));  f1[j]:=((rhs(fff[1,1]))^(2))/(2):f2[j]:=((rhs(fff[2,1]))^(2))/(2):f3[j]:=((rhs(fff[3,1]))^(2))/(2):  end do:   ll1:=[[Omega1[n],f1[n]] \$n=377..jmax]:  pp1:=plot(ll1, x=0..10,y=0..1,  style=point,symbol=solidcircle,symbolsize=4,color=red):    ll2:=[[Omega1[n],f2[n]] \$n=377..jmax]:  pp2:=plot(ll2, x=0..10,y=0..1,  style=point,symbol=solidcircle,symbolsize=4,color=red):    ll3:=[[Omega1[n],f3[n]] \$n=377..jmax]:  pp3:=plot(ll3, x=0..15,y=0..1,  style=point,symbol=solidcircle,symbolsize=4,color=red):       plot({  seq(seq(p1), seq(seq(pp1),seq(seq(pp2),seq(seq(pp3))  },style=point,title=`Pitchfork Diagram`);  Thanks for your help

How maple solve optimal control problem in deter...

Does any body have example of maple code for solving optimal control problem in deterministic model using Pontryagin's maximum (or minimum) principle?

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