Advanced Search

salim-barzani

1765 Reputation

9 Badges

1 years, 327 days
Contact salim-barzani

MaplePrimes Activity


These are questions asked by salim-barzani

ODE Test Fails for Solution...

salim-barzani 1765 Maple 2024
ode differential-equations odetest
May 01 2025
1 5

I’m trying to verify a solution given in the form from  using Maple's odeTest. Even though the paper claims the solution satisfies the ODE, Maple does not simplify the result to zero. Could someone explain why the test fails or suggest the correct way to verify it in Maple?

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

with(Physics)
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

_local(gamma)

Warning, A new binding for the name `gamma` has been created. The global instance of this name is still accessible using the :- prefix, :-`gamma`.  See ?protect for details.

  
> 

declare(u(x, t)); declare(U(xi)); declare(u(x, y, z, t)); declare(Q(xi)); declare(V(xi))

u(x, t)*`will now be displayed as`*u

  

U(xi)*`will now be displayed as`*U

  

u(x, y, z, t)*`will now be displayed as`*u

  

Q(xi)*`will now be displayed as`*Q

  

V(xi)*`will now be displayed as`*V

 (2)
> 

NULL
> 

ode := diff(G(xi), xi) = G(xi)*sqrt(A+B*G(xi)^2)

diff(G(xi), xi) = G(xi)*(A+B*G(xi)^2)^(1/2)

 (3)
> 

S1 := G(xi) = -sqrt(A/B)*csch(sqrt(A)*(xi+xi[0]))

G(xi) = -(A/B)^(1/2)*csch(A^(1/2)*(xi+xi[0]))

 (4)
> 

res := simplify(odetest(S1, ode))

(A/B)^(1/2)*csch(A^(1/2)*(xi+xi[0]))*(A^(1/2)*coth(A^(1/2)*(xi+xi[0]))+(A*coth(A^(1/2)*(xi+xi[0]))^2)^(1/2))

 (5)
> 

S2 := G(xi) = sqrt(-A/B)*sec(sqrt(-A)*(xi+xi[0]))

G(xi) = (-A/B)^(1/2)*sec((-A)^(1/2)*(xi+xi[0]))

 (6)
> 

res := simplify(odetest(S2, ode))

(-A/B)^(1/2)*sec((-A)^(1/2)*(xi+xi[0]))*((-A)^(1/2)*tan((-A)^(1/2)*(xi+xi[0]))-(-A*tan((-A)^(1/2)*(xi+xi[0]))^2)^(1/2))

 (7)
> 

S3 := G(xi) = sqrt(-A/B)*sech(sqrt(A)*(xi+xi[0]))

G(xi) = (-A/B)^(1/2)*sech(A^(1/2)*(xi+xi[0]))

 (8)
> 

res := simplify(odetest(S3, ode))

(-A^(1/2)*tanh(A^(1/2)*(xi+xi[0]))-(A*tanh(A^(1/2)*(xi+xi[0]))^2)^(1/2))*(-A/B)^(1/2)*sech(A^(1/2)*(xi+xi[0]))

 (9)
> 

S4 := G(xi) = sqrt(-A/B)*csc(sqrt(-A)*(xi+xi[0]))

G(xi) = (-A/B)^(1/2)*csc((-A)^(1/2)*(xi+xi[0]))

 (10)
> 

res := simplify(odetest(S4, ode))

(-(-A)^(1/2)*cot((-A)^(1/2)*(xi+xi[0]))-(-A*cot((-A)^(1/2)*(xi+xi[0]))^2)^(1/2))*(-A/B)^(1/2)*csc((-A)^(1/2)*(xi+xi[0]))

 (11)
> 

S5 := G(xi) = cos(sqrt(-A)*(xi+xi[0]))+sin(sqrt(-A)*(xi+xi[0]))

G(xi) = cos((-A)^(1/2)*(xi+xi[0]))+sin((-A)^(1/2)*(xi+xi[0]))

 (12)
> 

res := simplify(odetest(S5, ode))

(cos((-A)^(1/2)*(xi+xi[0]))-sin((-A)^(1/2)*(xi+xi[0])))*(-A)^(1/2)+(B*sin(2*(-A)^(1/2)*(xi+xi[0]))+A+B)^(1/2)*(-cos((-A)^(1/2)*(xi+xi[0]))-sin((-A)^(1/2)*(xi+xi[0])))

 (13)
> 

S6 := G(xi) = 1/(sqrt(B)*(xi+xi[0]))

G(xi) = 1/(B^(1/2)*(xi+xi[0]))

 (14)
> 

odetest(S6, subs(A = 0, ode))

-csgn(1/(xi+xi[0]))/(B^(1/2)*(xi+xi[0])^2)-1/(B^(1/2)*(xi+xi[0])^2)

 (15)
> 

S7 := G(xi) = 1/(sqrt(-B)*(xi+xi[0]))

G(xi) = 1/((-B)^(1/2)*(xi+xi[0]))

 (16)
> 

odetest(S7, subs(A = 0, ode))

-(-1/(xi+xi[0])^2)^(1/2)*xi[0]/((-B)^(1/2)*(xi+xi[0])^2)-(-1/(xi+xi[0])^2)^(1/2)*xi/((-B)^(1/2)*(xi+xi[0])^2)-1/((-B)^(1/2)*(xi+xi[0])^2)

 (17)
> 

ode2 := diff(G(xi), xi) = A+B*G(xi)^2

diff(G(xi), xi) = A+B*G(xi)^2

 (18)
> 

S8 := G(xi) = sgn(A)*sqrt(A/B)*tan(sqrt(A*B)*(xi+xi[0]))

G(xi) = sgn(A)*(A/B)^(1/2)*tan((A*B)^(1/2)*(xi+xi[0]))

 (19)
> 

res := simplify(odetest(S8, ode2))

(sgn(A)*(A*B)^(1/2)*(tan((A*B)^(1/2)*xi[0])^2+1)*(tan((A*B)^(1/2)*xi)^2+1)*(A/B)^(1/2)-A*((tan((A*B)^(1/2)*xi)+tan((A*B)^(1/2)*xi[0]))^2*sgn(A)^2+(tan((A*B)^(1/2)*xi[0])*tan((A*B)^(1/2)*xi)-1)^2))/(tan((A*B)^(1/2)*xi[0])*tan((A*B)^(1/2)*xi)-1)^2

 (20)
> 

NULL
> 

S9 := G(xi) = -sgn(A)*sqrt(A/B)*cot(sqrt(A*B)*(xi+xi[0]))

G(xi) = -sgn(A)*(A/B)^(1/2)*cot((A*B)^(1/2)*(xi+xi[0]))

 (21)
> 

res := simplify(odetest(S9, ode2))

(sgn(A)*(A*B)^(1/2)*(cot((A*B)^(1/2)*xi[0])^2+1)*(cot((A*B)^(1/2)*xi)^2+1)*(A/B)^(1/2)-A*((cot((A*B)^(1/2)*xi[0])*cot((A*B)^(1/2)*xi)-1)^2*sgn(A)^2+(cot((A*B)^(1/2)*xi[0])+cot((A*B)^(1/2)*xi))^2))/(cot((A*B)^(1/2)*xi[0])+cot((A*B)^(1/2)*xi))^2

 (22)
> 

NULL
> 

S9 := G(xi) = sgn(A)*sqrt(-A/B)*tanh(sqrt(-A*B)*(xi+xi[0]))

G(xi) = sgn(A)*(-A/B)^(1/2)*tanh((-A*B)^(1/2)*(xi+xi[0]))

 (23)
> 

res := simplify(odetest(S9, ode2))

(A*(sgn(A)^2-1)*cosh(2*(-A*B)^(1/2)*(xi+xi[0]))-sgn(A)^2*A+2*sgn(A)*(-A/B)^(1/2)*(-A*B)^(1/2)-A)/(1+cosh(2*(-A*B)^(1/2)*(xi+xi[0])))

 (24)
> 

NULL
> 

S10 := G(xi) = sgn(A)*sqrt(-A/B)*coth(sqrt(-A*B)*(xi+xi[0]))

G(xi) = sgn(A)*(-A/B)^(1/2)*coth((-A*B)^(1/2)*(xi+xi[0]))

 (25)
> 

odetest(S10, ode2)

(sgn(A)^2*A*cosh(2*(-A*B)^(1/2)*(xi+xi[0]))+sgn(A)^2*A-2*sgn(A)*(-A/B)^(1/2)*(-A*B)^(1/2)-A*cosh(2*(-A*B)^(1/2)*(xi+xi[0]))+A)/(-1+cosh(2*(-A*B)^(1/2)*(xi+xi[0])))

 (26)
> 

NULL
> 

S11 := G(xi) = -1/(B*(xi+xi[0]))

G(xi) = -1/(B*(xi+xi[0]))

 (27)
> 

odetest(S11, subs(A = 0, ode2))

0

 (28)
> 

S12 := G(xi) = A*(xi+xi[0])

G(xi) = A*(xi+xi[0])

 (29)
> 

odetest(S12, subs(B = 0, ode2))

0

 (30)

Download Z1.mw

ODE odetest not returning zero – possibl...

salim-barzani 1765 Maple 2024
ode assumptions differential-equations
May 01 2025
1 1

Why doesn't this ODE return zero when using odetest? Did I do something wrong?

Would you like help checking the equation or debugging the issue?

> 

restart
> 

with(PDEtools)
> 

declare(P(mu))

P(mu)*`will now be displayed as`*P

 (1)
> 

assume(A::real, r::real, rho::real, lambda::real)
> 

Psol := P(mu) = 2*A*lambda/((A^2+r)*exp(lambda*rho*mu)+r*exp(-lambda*rho*mu))

P(mu) = 2*A*lambda/((A^2+r)*exp(lambda*rho*mu)+r*exp(-lambda*rho*mu))

 (2)
> 

ode := (diff(P(mu), mu))^2-rho^2*P(mu)^2*(1+r*P(mu)^2) = 0

(diff(P(mu), mu))^2-rho^2*P(mu)^2*(1+r*P(mu)^2) = 0

 (3)
> 

res := odetest(Psol, ode)

4*A^6*rho^2*lambda^4*exp(6*lambda*rho*mu)/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4+8*r*A^4*rho^2*lambda^4*exp(6*lambda*rho*mu)/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4-24*A^4*lambda^4*rho^2*exp(4*lambda*rho*mu)*r/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4-4*A^6*rho^2*lambda^2*exp(6*lambda*rho*mu)/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4+4*A^2*r^2*rho^2*lambda^4*exp(6*lambda*rho*mu)/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4-8*A^2*lambda^4*rho^2*exp(4*lambda*rho*mu)*r^2/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4+4*A^2*r^2*rho^2*lambda^4*exp(2*lambda*rho*mu)/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4-8*r*A^4*rho^2*lambda^2*exp(6*lambda*rho*mu)/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4-8*A^4*lambda^2*rho^2*exp(4*lambda*rho*mu)*r/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4-4*A^2*r^2*rho^2*lambda^2*exp(6*lambda*rho*mu)/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4-8*A^2*lambda^2*rho^2*exp(4*lambda*rho*mu)*r^2/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4-4*A^2*r^2*rho^2*lambda^2*exp(2*lambda*rho*mu)/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4

 (4)
> 

simplify(res)

4*lambda^2*exp(2*lambda*rho*mu)*(((-2*lambda^2-2)*r^2+(-6*lambda^2-2)*A^2*r)*exp(2*lambda*rho*mu)+(lambda+1)*((A^2+r)^2*exp(4*lambda*rho*mu)+r^2)*(lambda-1))*A^2*rho^2/((A^2+r)*exp(2*lambda*rho*mu)+r)^4

 (5)
> 

P_hyper := P(mu) = 2*A*lambda/((A^2+r)*cosh(rho*mu)+(A^2-r)*sinh(rho*mu))

P(mu) = 2*A*lambda/((A^2+r)*cosh(rho*mu)+(A^2-r)*sinh(rho*mu))

 (6)
> 

res_hyper := simplify(odetest(P_hyper, ode), symbolic)

-16*A^4*lambda^2*rho^2*r*(lambda^2+1)/((A^2+r)*cosh(rho*mu)+(A^2-r)*sinh(rho*mu))^4

 (7)
 

NULL

Download ode.mw

Verifying ODE Solution and Issues with A...

salim-barzani 1765 Maple 2024
ode assumptions differential-equations
April 30 2025
1 1

I’m trying to test a specific function as a solution to a nonlinear ODE in Maple. The equation is of the Riccati type, and my candidate solution involves parameters A, B, and C.

I've used assuming to specify the condition (4AC−B2)>0 and (4AC - B^2) <0, but when I use odetest to verify the solution, I still get a nonzero result. Additionally, when I apply the assumption, Maple sometimes introduces a negation sign in the output (e.g., changing sqrt(...) into -sqrt(...)), which wasn't part of the original solution.

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

with(Physics)
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

E := diff(G(xi), xi) = A+B*G(xi)+C*G(xi)^2

diff(G(xi), xi) = A+B*G(xi)+C*G(xi)^2

 (2)
> 

> 

S1 := G(xi) = (sqrt(4*A*C-B^2)*tan((1/2)*sqrt(4*A*C-B^2)*(d[0]+xi))-B)/(2*C)

G(xi) = (1/2)*((4*A*C-B^2)^(1/2)*tan((1/2)*(4*A*C-B^2)^(1/2)*(d[0]+xi))-B)/C

 (3)
> 

odetest(S1, E)

0

 (4)
> 

> 

S2 := G(xi) = -(sqrt(4*A*C-B^2)*cot((1/2)*sqrt(4*A*C-B^2)*(d[0]+xi))+B)/(2*C)

G(xi) = -(1/2)*((4*A*C-B^2)^(1/2)*cot((1/2)*(4*A*C-B^2)^(1/2)*(d[0]+xi))+B)/C

 (5)
> 

odetest(S2, E)

0

 (6)
> 

assume(4*A*C-B^2 < 0)
> 

S3 := G(xi) = -(sqrt(4*A*C-B^2)*tanh((1/2)*sqrt(4*A*C-B^2)*(d[0]+xi))+B)/(2*C)

G(xi) = -(1/2)*((4*A*C-B^2)^(1/2)*tanh((1/2)*(4*A*C-B^2)^(1/2)*(d[0]+xi))+B)/C

 (7)
> 

odetest(S3, E)

-2*A+(1/2)*B^2/C

 (8)

Download A2.mw

Why the subs command not apply ?...

salim-barzani 1765 Maple 2024
radical substitution subs
April 29 2025
2 7

i did every thing coreectly but nothing happen not apply where is my mistake?

> 

``
> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

with(Physics)
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

NULL
> 

S := (diff(G(xi), xi))^2-r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2) = 0

(diff(G(xi), xi))^2-r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2) = 0

 (2)
> 

SS := diff(G(xi), xi) = sqrt(r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2))

diff(G(xi), xi) = (r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2))^(1/2)

 (3)
> 

Se := sqrt(r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2)) = diff(G(xi), xi)

(r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2))^(1/2) = diff(G(xi), xi)

 (4)
> 

dub := diff(SS, xi)

diff(diff(G(xi), xi), xi) = (1/2)*(2*r^2*G(xi)*(a+b*G(xi)+l*G(xi)^2)*(diff(G(xi), xi))+r^2*G(xi)^2*(b*(diff(G(xi), xi))+2*l*G(xi)*(diff(G(xi), xi))))/(r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2))^(1/2)

 (5)
> 

Dubl2 := simplify(diff(diff(G(xi), xi), xi) = (1/2)*(2*r^2*G(xi)*(a+b*G(xi)+l*G(xi)^2)*(diff(G(xi), xi))+r^2*G(xi)^2*(b*(diff(G(xi), xi))+2*l*G(xi)*(diff(G(xi), xi))))/(r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2))^(1/2))

diff(diff(G(xi), xi), xi) = (1/2)*r^2*G(xi)*(diff(G(xi), xi))*(4*l*G(xi)^2+3*b*G(xi)+2*a)/(r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2))^(1/2)

 (6)
> 

subs(SA, Dubl2)

diff((r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2))^(1/2), xi) = (1/2)*r^2*G(xi)*(4*l*G(xi)^2+3*b*G(xi)+2*a)

 (7)
> 

subs(Se, Dubl2)

diff(diff(G(xi), xi), xi) = (1/2)*r^2*G(xi)*(diff(G(xi), xi))*(4*l*G(xi)^2+3*b*G(xi)+2*a)/(r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2))^(1/2)

 (8)
> 

subs(lhs(Se) = rhs(Se), Dubl2)

diff(diff(G(xi), xi), xi) = (1/2)*r^2*G(xi)*(diff(G(xi), xi))*(4*l*G(xi)^2+3*b*G(xi)+2*a)/(r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2))^(1/2)

 (9)
 

NULL

Download subs.mw

Help with Solving ODE and Representing &...

salim-barzani 1765 Maple 2024
ode dsolve differential-equations
April 29 2025
2 6

I tried solving this ODE, but my result is very different from the expected one. How can I correctly obtain the solution? Also, is there a way to include both the positive and negative signs (±) in the equation so that the final result reflects both possibilities?

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

with(Physics)
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

_local(gamma)

Warning, A new binding for the name `gamma` has been created. The global instance of this name is still accessible using the :- prefix, :-`gamma`.  See ?protect for details.

  
> 

declare(Omega(x, t)); declare(U(xi)); declare(u(x, y, z, t)); declare(Q(xi)); declare(V(xi))

Omega(x, t)*`will now be displayed as`*Omega

  

U(xi)*`will now be displayed as`*U

  

u(x, y, z, t)*`will now be displayed as`*u

  

Q(xi)*`will now be displayed as`*Q

  

V(xi)*`will now be displayed as`*V

 (2)
> 

``
> 

ode := f*g^3*(diff(diff(U(xi), xi), xi))-4*f*p*U(xi)-6*k*l*U(xi)-f^3*g*(diff(diff(U(xi), xi), xi))+6*f*g*U(xi)^2 = 0

f*g^3*(diff(diff(U(xi), xi), xi))-4*f*p*U(xi)-6*k*l*U(xi)-f^3*g*(diff(diff(U(xi), xi), xi))+6*f*g*U(xi)^2 = 0

 (3)
> 

S := (diff(G(xi), xi))^2-r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2) = 0

(diff(G(xi), xi))^2-r^2*G(xi)^2*(a+b*G(xi)+l*G(xi)^2) = 0

 (4)
> 

S1 := dsolve(S, G(xi))

G(xi) = (1/2)*(-b+(-4*a*l+b^2)^(1/2))/l, G(xi) = -(1/2)*(b+(-4*a*l+b^2)^(1/2))/l, G(xi) = -4*a*exp(c__1*r*a^(1/2))/(exp(xi*r*a^(1/2))*(4*a*l-b^2+2*b*exp(c__1*r*a^(1/2))/exp(xi*r*a^(1/2))-(exp(c__1*r*a^(1/2)))^2/(exp(xi*r*a^(1/2)))^2)), G(xi) = -4*a*exp(xi*r*a^(1/2))/(exp(c__1*r*a^(1/2))*(4*a*l-b^2+2*b*exp(xi*r*a^(1/2))/exp(c__1*r*a^(1/2))-(exp(xi*r*a^(1/2)))^2/(exp(c__1*r*a^(1/2)))^2))

 (5)
> 

S2 := S1[3]

G(xi) = -4*a*exp(c__1*r*a^(1/2))/(exp(xi*r*a^(1/2))*(4*a*l-b^2+2*b*exp(c__1*r*a^(1/2))/exp(xi*r*a^(1/2))-(exp(c__1*r*a^(1/2)))^2/(exp(xi*r*a^(1/2)))^2))

 (6)
> 

normal(G(xi) = -4*a*exp(c__1*r*a^(1/2))/(exp(xi*r*a^(1/2))*(4*a*l-b^2+2*b*exp(c__1*r*a^(1/2))/exp(xi*r*a^(1/2))-(exp(c__1*r*a^(1/2)))^2/(exp(xi*r*a^(1/2)))^2)), ':-expanded')

G(xi) = 4*a*exp(c__1*r*a^(1/2))*exp(xi*r*a^(1/2))/(-4*a*l*(exp(xi*r*a^(1/2)))^2+b^2*(exp(xi*r*a^(1/2)))^2-2*b*exp(c__1*r*a^(1/2))*exp(xi*r*a^(1/2))+(exp(c__1*r*a^(1/2)))^2)

 (7)
> 

simplify(G(xi) = 4*a*exp(c__1*r*a^(1/2))*exp(xi*r*a^(1/2))/(-4*a*l*(exp(xi*r*a^(1/2)))^2+b^2*(exp(xi*r*a^(1/2)))^2-2*b*exp(c__1*r*a^(1/2))*exp(xi*r*a^(1/2))+(exp(c__1*r*a^(1/2)))^2))

G(xi) = -4*a*exp(a^(1/2)*r*(c__1+xi))/(4*a*l*exp(2*xi*r*a^(1/2))-b^2*exp(2*xi*r*a^(1/2))+2*b*exp(a^(1/2)*r*(c__1+xi))-exp(2*c__1*r*a^(1/2)))

 (8)
> 

convert(%, trig)

G(xi) = -4*a*(cosh(a^(1/2)*r*(c__1+xi))+sinh(a^(1/2)*r*(c__1+xi)))/(4*a*l*(cosh(2*xi*r*a^(1/2))+sinh(2*xi*r*a^(1/2)))-b^2*(cosh(2*xi*r*a^(1/2))+sinh(2*xi*r*a^(1/2)))+2*b*(cosh(a^(1/2)*r*(c__1+xi))+sinh(a^(1/2)*r*(c__1+xi)))-cosh(2*c__1*r*a^(1/2))-sinh(2*c__1*r*a^(1/2)))

 (9)
> 

convert(S1[3], trig)

G(xi) = -4*a*(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2)))/((cosh(xi*r*a^(1/2))+sinh(xi*r*a^(1/2)))*(4*a*l-b^2+2*b*(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2)))/(cosh(xi*r*a^(1/2))+sinh(xi*r*a^(1/2)))-(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2)))^2/(cosh(xi*r*a^(1/2))+sinh(xi*r*a^(1/2)))^2))

 (10)
> 

simplify(G(xi) = -4*a*(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2)))/((cosh(xi*r*a^(1/2))+sinh(xi*r*a^(1/2)))*(4*a*l-b^2+2*b*(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2)))/(cosh(xi*r*a^(1/2))+sinh(xi*r*a^(1/2)))-(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2)))^2/(cosh(xi*r*a^(1/2))+sinh(xi*r*a^(1/2)))^2)))

G(xi) = -4*a*(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2)))*(cosh(xi*r*a^(1/2))+sinh(xi*r*a^(1/2)))/((4*a*l-b^2)*cosh(xi*r*a^(1/2))^2+((8*a*l-2*b^2)*sinh(xi*r*a^(1/2))+2*b*(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2))))*cosh(xi*r*a^(1/2))+(4*a*l-b^2)*sinh(xi*r*a^(1/2))^2+2*b*(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2)))*sinh(xi*r*a^(1/2))-(cosh(c__1*r*a^(1/2))+sinh(c__1*r*a^(1/2)))^2)

 (11)
   

Download tt.mw

First 14 15 16 17 18 19 20 Last Page 16 of 42