Maple 2021 Questions and Posts

These are Posts and Questions associated with the product, Maple 2021

This expression is easy i think but i can't get any results with same shape  how i can simplify to the same equation in the paper

i am looking for equation 9 and every thing is clear how i can get

mp1.mw

intersections := proc(P, Q, T)
local R, W, w, t, a, b, sol, buff, v;
sol := NULL;
if T = Y then W := X; else
W := Y; end if;
R := resultant(P, Q, T);
print(`Résultant :`); print(R);
w := fsolve(R, W); t := NULL;
for v in [w] do t := t, fsolve(subs(W = v, P), T); end do;
for a in {w} do for b in {t} do if T = Y then
buff := abs(subs(X = a, Y = b, P)) + abs(subs(X = a, Y = b, Q));
printf(`X=%a,   Y=%a   --->  %a\\n`, a, b, buff); if buff < 1/100000000 then sol := sol, [a, b]; end if;
else buff := abs(subs(X = b, Y = a, P)) + abs(subs(X = b, Y = a, Q));
printf(`X=%a,   Y=%a   --->  %a\\n `, a, b, buff); if buff < 1/100000000 then sol := sol, [b, a]; end if; end if; end do; end do; printf(`Nombre de solutions :  %a\\n`, nops({sol})); print({sol}); end proc:
intersections(X^2 + Y^2 - 1, X - Y, X);
X=-.7071067812,   Y=-.7071067812   --->  0.\n 
I do not wish to find \n in the answer

 In the calculation process, I selected (num=5). How can I detect the maximum value of num to ensure the series solution would be converged?

seried.mw

restart;
with(geometry);
with(plots);
Bl := color = black;
y0 := x -> -ln(1 - exp(-x));
y0 := proc (x) options operator, arrow; -ln(1-exp(-x)) end proc

y1 := x -> -ln(-1 + exp(-x));
y1 := proc (x) options operator, arrow; -ln(-1+exp(-x)) end proc

y2 := x -> -ln(1 + exp(-x));
y2 := proc (x) options operator, arrow; -ln(1+exp(-x)) end proc

p := plot(y0(x), x = 0.02 .. 4, scaling = constrained, color = blue);
p1 := plot(y2(x), x = -4 .. 4, scaling = constrained, color = green);
p2 := plot(y1(x), x = -4 .. 0, scaling = constrained, color = red);
display({p, p1, p2}, view = [-4 .. 4, -4 .. 5]);
Calculate its area; Thank you.

On donne un cercle fixe de diamètre AB, un point M variable sur ce cercle et on construit un carré de sens direct AMNP; Trouver les lieux des points N et P.
restart;
with(plots);
r := 1;
A := [-r, 0];
B := [r, 0];
M := [r*cos(theta), r*sin(theta)];
N := [r*cos(theta) - r*sin(theta), r*sin(theta) + r*cos(theta)];
P := [-r*cos(theta) - r*sin(theta), r*cos(theta) - r*sin(theta)];
c1 := `~`[plottools]*circle([0, 0], r, color = blue);
plot1 := plot(c1, color = blue);
plot2 := animate([N[1], N[2], theta = 0 .. 2*Pi], color = red, thickness = 2);
plot3 := animate([P[1], P[2], theta = 0 .. 2*Pi], color = green, thickness = 2);
display(plot1, plot2, plot3);
Would you like to improve this code so it works. Thank you.
 

i have solution of ODE but again i want take derivative from solution function F then i want take reciprocal of derivative
if F'=G then i want 1/F'=1/G like that i want all solution by list and if possible don't give the parameter a sequence  it will be better

thanks for any help

K := diff(G(xi), xi $ 2) = -lambda*diff(G(xi), xi) - mu;
                 2                                    
                d                    / d        \     
          K := ----- G(xi) = -lambda |---- G(xi)| - mu
                   2                 \ dxi      /     
                dxi                                   

V:= [seq](-1..1, 1/2);
                          [    -1     1   ]
                     V := [-1, --, 0, -, 1]
                          [    2      2   ]

interface(rtablesize= nops(V)^3):
DataFrame(
    <seq(seq(<a | b | rhs(dsolve(eval(K, [lambda,mu]=~ [a,b])))>, a= V), b= V)>,
    columns= [lambda, mu, F]
);

loading

Error occurred during PDF generation. Please refresh the page and try again

Hi
my odetest must give me zero everything is true but still not simplify the function with power include 1/n  not do cancelation even

test_sol_for_PDE.mw

Hello,

How can I reduce time calculations for the integral process?

Determining H[1] and HH[1] is very boring!!

 

time_consuming_calculations.mw

i have ODE equation i want a list of function solution when the parameter change then the solution is change too,so i wan the out come function and also show the parameter too i have idea but i can't write a generator function for it

restart

K := diff(F(xi), xi) = A+B*F(xi)+C*F(xi)^2

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

(1)

dsolve(K, F(xi))

F(xi) = -(1/2)*(-tan((1/2)*_C1*(4*A*C-B^2)^(1/2)+(1/2)*xi*(4*A*C-B^2)^(1/2))*(4*A*C-B^2)^(1/2)+B)/C

(2)

NULL

i want something like this table

Download find_generator_ode_function_.mw

please someone help for writing this program is importan

restart

``

B := (sum(a__n*exp(n*x), n = -c .. p))/(sum(b__m*exp(m*x), m = -d .. q))

(exp((p+1)*x)/(exp(x)-1)-exp(-c*x)/(exp(x)-1))*a__n/((exp((q+1)*x)/(exp(x)-1)-exp(-d*x)/(exp(x)-1))*b__m)

(1)

 

NULL

Download open_series_and_take_derivative.mw

restart;
_local(D, O);
with(Student:-MultivariateCalculus);
A := [0, 0, 0];
B := [a, 0, 0];
C := [a, b, 0];
D := [0, b, 0];
S := [0, 0, h];
O := [x, y, z];
lineSC := Line(S, C);
lineSD := Line(S, D);
H := Projection(A, lineSC);
K := Projection(A, lineSD);
OH := H - O;
OK := K - O;
OC := C - O;
M := Matrix([OH, OK, OC]);
O := eval(O, %);
simplify(Distance(O, H));
                               O

Error, invalid input: eval received Matrix(3, 3, {(1, 1) = -x+h^2*a/(a^2+b^2+h^2), (1, 2) = -y+h^2*b/(a^2+b^2+h^2), (1, 3) = -z+h*(a^2+b^2)/(a^2+b^2+h^2), (2, 1) = -x, (2, 2) = -y+h^2*b/(b^2+h^2), (2, 3) = -z+h*b^2/(b^2+h^2), (3, 1) = -x+a, (3, 2) = -y+b, (3, 3) = -z}), which is not valid for its 2nd argument, eqns
How to correct this error ? Thank you.

restart;

local gamma;

gamma

(1)

with(Plot)

 

params := {alpha = 2.5, k = 3, w = 2, beta[3] = 3, beta[4] = 1.7,theta=0,gamma=1};

{alpha = 2.5, gamma = 1, k = 3, theta = 0, w = 2, beta[3] = 3, beta[4] = 1.7}

(2)

xi := sqrt(-1/(72*alpha*beta[4]+72*gamma*beta[4]))*(2*alpha*k*t+x)

(-1/(72*alpha*beta[4]+72*gamma*beta[4]))^(1/2)*(2*alpha*k*t+x)

(3)

 

sol1 := [U(xi), -k*x -(9*alpha*k^2*beta[4] + 2*beta[3]^2)/(9*beta[4])*t + theta];

[U((-1/(72*alpha*beta[4]+72*gamma*beta[4]))^(1/2)*(2*alpha*k*t+x)), -k*x-(1/9)*(9*alpha*k^2*beta[4]+2*beta[3]^2)*t/beta[4]+theta]

(4)

 

sol2 := eval(sol1, U(xi) = -beta[3]/(3*beta[4]) + beta[3]*sinh(xi)/(6*beta[4]*cosh(xi)) + beta[3]*cosh(xi)/(6*beta[4]*sinh(xi)));

[-(1/3)*beta[3]/beta[4]+(1/6)*beta[3]*sinh((-1/(72*alpha*beta[4]+72*gamma*beta[4]))^(1/2)*(2*alpha*k*t+x))/(beta[4]*cosh((-1/(72*alpha*beta[4]+72*gamma*beta[4]))^(1/2)*(2*alpha*k*t+x)))+(1/6)*beta[3]*cosh((-1/(72*alpha*beta[4]+72*gamma*beta[4]))^(1/2)*(2*alpha*k*t+x))/(beta[4]*sinh((-1/(72*alpha*beta[4]+72*gamma*beta[4]))^(1/2)*(2*alpha*k*t+x))), -k*x-(1/9)*(9*alpha*k^2*beta[4]+2*beta[3]^2)*t/beta[4]+theta]

(5)

 

solnum :=eval(sol2, params);

[-.5882352940+(.2941176471*I)*sin(.7247137946*t+0.4831425297e-1*x)/cos(.7247137946*t+0.4831425297e-1*x)-(.2941176471*I)*cos(.7247137946*t+0.4831425297e-1*x)/sin(.7247137946*t+0.4831425297e-1*x), -3*x-23.67647059*t]

(6)

plots:-complexplot3d(solnum, x = -50.. 50, t = -50..50);

Warning, unable to evaluate the function to numeric values in the region; complex values were detected

 

 

NULL


if there is any other way for graph please share with me

Download complexplot3d.mw

restart;
with(Plot);
params := {alpha = 2.5, k = 3, w = 2, beta[3] = 3, beta[4] = 1.7};
xi := beta[3]*(2*alpha*k*t + x)*sqrt(1/(36*alpha*beta[4] + 36*gamma*beta[4]));
params := {alpha = 2.5, k = 3, w = 2, beta[3] = 3, beta[4] = 1.7}

          xi := beta[3] (2 alpha k t + x) 

                                                 (1/2)
            /                 1                 \     
            |-----------------------------------|     
            \36 alpha beta[4] + 36 gamma beta[4]/     


sol1n := u(x, t) = U(xi)*exp((-sqrt(1/(36*alpha*beta[4] + 36*gamma*beta[4]))*x + w*t + theta)*I);
                     /                          
                     |                          
 sol1n := u(x, t) = U|beta[3] (2 alpha k t + x) 
                     \                          

                                        (1/2)\    /  /
   /                 1                 \     |    |  |
   |-----------------------------------|     | exp|I |
   \36 alpha beta[4] + 36 gamma beta[4]/     /    \  \
                                       (1/2)                \\
  /                 1                 \                     ||
 -|-----------------------------------|      x + w t + theta||
  \36 alpha beta[4] + 36 gamma beta[4]/                     //



plot3d(rhs(sol1n), x = 0 .. 250, t = 0 .. 4);

how plot the the solution of PDE of this kind of function?

Download plot.mw

before run file remove all (:) i want calculate equation but with a condition for example: when a=4 then find other parameter in my equation with respect to a=4 find other

usesol.mw

when i finding parameter i want just choose a case for example a_1=a_1  and any other case a_2=0,and remove other case how i can do in maple

restart

with(PDEtools)

undeclare(prime)

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

(1)

with(DEtools)

with(DifferentialAlgebra)

"with(Student[ODEs][Solve]): "

with(IntegrationTools)

with(inttrans)

with(PDEtools)

with(Physics)

with(PolynomialTools)

with(RootFinding)

with(SolveTools)

with(LinearAlgebra)

with(sumtools)

``

ode := F(xi)^5*a[4]+F(xi)^4*a[3]+F(xi)^3*a[2]+(-k^2*a[1]+(diff(diff(F(xi), xi), xi))*a[5]-w)*F(xi)^2+(1/2)*F(xi)*(diff(diff(F(xi), xi), xi))*a[1]-(1/4)*(diff(F(xi), xi))^2*a[1] = 0

NULL

L := convert((cosh(xi)+sinh(xi))/(cosh(xi)-sinh(xi)), trig)

"Q(xi):=L:"

S := sum(A[i]*Q(xi)^i, i = 0 .. 1)+sum(B[i]*Q(xi)^(-i), i = 1 .. 1)

``

(2)

S

K := F(xi) = S

F1 := eval(ode, K)

simplify(%)

P := numer(lhs())*denom(rhs()) = numer(rhs())*denom(lhs())

Warning,  computation interrupted

 

NULL

solve(identity(P, xi), {k, w, A[0], A[1], B[1], a[1], a[2], a[3], a[4], a[5]})

Warning, solutions may have been lost

 

{k = k, w = w, A[0] = 0, A[1] = A[1], B[1] = 0, a[1] = a[1], a[2] = a[2], a[3] = a[3], a[4] = a[4], a[5] = a[5]}, {k = k, w = -4*A[0]*a[5], A[0] = A[0], A[1] = A[1], B[1] = B[1], a[1] = 0, a[2] = -4*a[5], a[3] = 0, a[4] = 0, a[5] = a[5]}, {k = k, w = (1/2)*A[0]*(3*k^2*A[0]^2*a[4]+2*k^2*A[0]*a[3]+k^2*a[2]+4*k^2*a[5]+2*A[0]^2*a[4]+2*A[0]*a[3]+2*a[2]), A[0] = A[0], A[1] = 0, B[1] = 0, a[1] = -(1/2)*A[0]*(3*A[0]^2*a[4]+2*A[0]*a[3]+a[2]+4*a[5]), a[2] = a[2], a[3] = a[3], a[4] = a[4], a[5] = a[5]}, {k = k, w = w, A[0] = A[0], A[1] = 0, B[1] = 0, a[1] = a[1], a[2] = (-A[0]^3*a[4]+k^2*a[1]-A[0]^2*a[3]+w)/A[0], a[3] = a[3], a[4] = a[4], a[5] = a[5]}, {k = k, w = 4*A[1]*a[5]+4*B[1]*a[5], A[0] = -A[1]-B[1], A[1] = A[1], B[1] = B[1], a[1] = 0, a[2] = -4*a[5], a[3] = 0, a[4] = 0, a[5] = a[5]}, {k = k, w = -k^2*a[1]-4*A[0]*a[5]+a[1], A[0] = A[0], A[1] = (1/4)*A[0]^2/B[1], B[1] = B[1], a[1] = a[1], a[2] = -4*a[5], a[3] = 0, a[4] = 0, a[5] = a[5]}, {k = k, w = w, A[0] = 2*B[1], A[1] = B[1], B[1] = B[1], a[1] = a[1], a[2] = (1/2)*(k^2*a[1]+w-a[1])/B[1], a[3] = 0, a[4] = 0, a[5] = -(1/8)*(k^2*a[1]+w-a[1])/B[1]}, {k = k, w = w, A[0] = A[0], A[1] = B[1], B[1] = B[1], a[1] = 0, a[2] = w/A[0], a[3] = 0, a[4] = 0, a[5] = -(1/4)*w/A[0]}, {k = k, w = 0, A[0] = 0, A[1] = B[1], B[1] = B[1], a[1] = 0, a[2] = a[2], a[3] = 0, a[4] = 0, a[5] = -(1/4)*a[2]}

(3)

Download choose_case.mw

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