Items tagged with differential_equation


Just thought I'd put a quick one in. I'm trying to solve the Schrodinger equation given as:

schro := {diff(psi(x), x, x)-((b^2-a*(2*p+3))*x^2+2*ab*x^4+a^2*x^6-energy)*psi(x) = 0};

under the constraint energy=(2p+1)b

I'm trying to plot this for a range of values of the parameters a,b and fixed p=0,1.

I'm aiming to get a solution of the form

psi(x)=(x^p) exp((-a(x^4))/4)-(b(x^2)/2)

and plotting it.

Thanks in advance

I am trying to solve in Maple the system 
d{x}/dt =(1  1 \\1  -1).{x}
with initial conditions {x(0)} =(1 \\ -1),
where {x} is a vector.

This is what I did up to now


but I am not sure how to correctly input the initial conditions to find a solution to the problem. I would appreciate any help provided.

i want to write the result of a calculation to a file in a way that i can be able to call them later. for example :

n := 40; h := 40;
a := h*i/(2*n);

sys1 := [diff(x(t), t) = 2*t+1, diff(y(t), t) = 1+5*t, x(0) = 1, y(1) = 0];

for i from 0 by .5 to 1 do res := dsolve(sys1, numeric); res(a) end do;

i would like to write just the values of t and y(t) to a file/vector or whatever.

Thx in advance

Hello all
I want to integrate an equation involving different terms (some of them involve derivatives) the following picture shows the expression and the end result. I can do it manually by multiplying both sides with u'. but how can acheive that in maple


Eq4 := diff(u(xi), xi, xi) = a[0]+a[1]*u(xi)+a[2]*u(xi)^2; Eq5 := int(Eq4, xi); simplify(%)

diff(diff(u(xi), xi), xi) = a[0]+a[1]*u(xi)+a[2]*u(xi)^2


Error, (in int) wrong number (or type) of arguments: wrong type of integrand passed to indefinite integration.


diff(diff(u(xi), xi), xi) = a[0]+a[1]*u(xi)+a[2]*u(xi)^2





I have tried to solve the following ode equation, but I have got error. What is the potencial problem?




hi..i have a problem for solving this nonlinear differential

restart; Digite := 200; L := 100*10^(-9)



EQ11 := -3.000000000*10^(-8)+3.815358072*sin(3.141592654*10^7*x)+9.534375000*10^(-30)*(diff(w(x), x, x, x, x))-2.383593750*10^(-60)*(diff(w(x), x, x, x, x, x, x))-5.085000000*10^(-13)*(diff(w(x), x))*(diff(u(x), x, x))-7.627500000*10^(-13)*(diff(w(x), x))^2*(diff(w(x), x, x))-5.085000000*10^(-13)*(diff(w(x), x, x))*(diff(u(x), x))+0.2410290000e-5*(diff(w(x), x, x)):

EQ2 := 5.650000000*10^(-20)*(diff(u(x), x, x, x, x))-226000000000*(diff(u(x), x, x))-226000000000*(diff(w(x), x))*(diff(w(x), x, x)):

dsys3 := {EQ11, EQ2, u(0) = 0, u(L) = 0, w(0) = 0, w(L) = 0, (D(u))(0) = 0, (D(u))(L) = 0, ((D@@2)(w))(0) = 0, ((D@@2)(w))(L) = 0, ((D@@4)(w))(0) = 0, ((D@@4)(w))(L) = 0}; res := dsolve(dsys3, numeric, initmesh = 1024, abserr = 0.1e-4); res(0.1e-9)



############################################################CHANGE OF VARIABLE:::           x=y*L

bcs := {u(0) = 0, u(L) = 0, w(0) = 0, w(L) = 0, (D(u))(0) = 0, (D(u))(L) = 0, ((D@@2)(w))(0) = 0, ((D@@2)(w))(L) = 0, ((D@@4)(w))(0) = 0, ((D@@4)(w))(L) = 0}; sys := {EQ11, EQ2}; sys2 := PDEtools:-dchange({x = L*y, u(x) = g2(y), w(x) = g1(y)}, sys, [g1, g2, y]); solve(sys2, {diff(g2(y), y, y, y, y), diff(g1(y), y, y, y, y, y, y)}); bcs3 := {g1(0) = 0, g1(1) = 0, g2(0) = 0, g2(1) = 0, (D(g2))(0) = 0, (D(g2))(1) = 0, ((D@@2)(g1))(0) = 0, ((D@@2)(g1))(1) = 0, ((D@@4)(g1))(0) = 0, ((D@@4)(g1))(1) = 0}; res3 := dsolve(`union`(sys2, bcs3), numeric, maxmesh = 2024, abserr = 0.1e-4); plots:-odeplot(res3, [seq([y, (cat(g, i))(y)], i = 1 .. 2)], 0 .. 1)

Error, (in plots/odeplot) input is not a valid dsolve/numeric solution





please help me



Hello guys


I am trying to solve a non-linear 2nd order diffential equation in order to describe the turbulence phenomena for tip vortices .

The initial conditions that i have are



Moreover i know that b from 0 to 1 equals one and then it  increases propably parabololoid(from the experimntal measurements)with respect o Re(Reynolds)

I tried to solve the eqution using maple solve de interactivelly but doesnt seem to work

Do you have any suggestions?

Thank you


I run into a problem that really suprised me. I have a program that solves a system of differential equations with different initial conditions. I wrote a cycle that goes through initial conditions, solves differential equations and saves the picture (displaying dynamic behaviour of the system) in the given directory. All seemed fine and working until I once checked one of the pictures by running the program on the only one initial condition. It turned out that the picture program gave me this time is not the one that program gave me earlier (while running through cycle). So I panicked and started checking other pictures and it turned out that some of them are right and some of them are not, remarkably, with no particular pattern.

I reckon that I somehow need to manage the memory, clear it after every iteration. (I'm not absolutely sure that problem is here but I just don't have another explanation why this thing could happen.)

i want a scheme of fractional differential equation so that i solve my questions and make a code of it.

please provide me the scheme





Can we calculate the following equations in Maple?

Substituting equations (21) and (22) into (17), and then obtain equation (23). How to do that? I have done this, but the results are complex and large. They are not in a sum form, but in an expansion form. The reference and the maple file are attached.

Hope for your help.

Best wishes,




Here is my question.


convert(diff(lambda(t-t1), t), diff)

eval(diff(lambda(t2), t2), {t2 = t-t1})


subs(lamda(t-t1) = sin(t-t1), %)

eval(diff(lambda(t2), t2), {t2 = t-t1})



I am trying to substitute value of lambda(t-t1) further but it is not taking the value.

Thanks in advance.





maple with collocation and galerkin methods

please help me with writing the cods


Hello everyone,

I have a problem with my  code, breif this is the equation that I want to solve 

x^2*(diff(y(x), x, x))+50*x*(diff(y(x), x))-35*y(x) = (1-exp(x+1))/(x+1)+(x^2+50*x-35)*exp(x)+int(exp(xt)*y(t), t = 0 .. 1), x = 0 .. 1

but the problem is that I don't know how to code the integral please guys help me 

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