salim-barzani

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These are questions asked by salim-barzani

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

when i do the convert in maple to latex  is do but not fully simplify and some kind of clearer must write for paper and i must do this case by case by hand but how i can simplify before i convert to latex and remove all extra thing like multiply between two squar root


 

restart

K := [A[1] = 0, A[0] = 0, B[1] = `&-+`(sqrt(2)*sqrt(a[5])/sqrt(a[4])), k = k, a[2] = -a[5], w = -2*a[5]*a[3]*(4*k^2-1)/(3*a[4]), a[1] = 8*a[5]*a[3]/(3*a[4]), v = 2*a[1]*k]

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

(1)

latex(K)

\left[A_{1} = 0, A_{0} = 0, B_{1} =
\mp \frac{\sqrt{2}\, \sqrt{a_{5}}}{\sqrt{a_{4}}}, k = k, a_{2} =
-a_{5}, w = -\frac{2 a_{5} a_{3} \left(4 k^{2}-1\right)}{3 a_{4}},
a_{1} = \frac{8 a_{5} a_{3}}{3 a_{4}}, v = 2 a_{1} k\right]

 

NULL


 

Download K.mw

i have a generator function but in out come i have phi(p_1,p_2,p_3, so on )=** result is clear but this p_1 and p_2 in not shown i want to be shown in my outcome

generate_solution.mw

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

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