How to find an explicit function when using Runge-Kutta or one of the pertinent codes in Matlab (ode45)

Dear scholars,

I have a question which is almost trivial, but I like to make a shot for this;

I need an explicit answer function. On the other hand, Runge-Kutta, DQM, any other numerical methods or even the available codes like ode23, 45; all give us the numerical values of the pertinent function. But, I need explicit function in temporal domain, since I need to take derivative and apply other algebraic operations for further findings and survey.

Any ideas?

Answer 1

[James Tursa]

Symbolic Toolbox

doc dsolve

https://www.mathworks.com/help/symbolic/dsolve.html

[Alireza Babaei]

Thanks ,

since my ode is nonlinear, Matlab can not find the solution symbollically

[James Tursa]

There may not be an explicit solution for your ode. What is it?

[Alireza Babaei]

James,

Here is the code I have tried including the nonlinear equation, I have

clc
clear all
close all

syms t y(t)
c = 7.5;
m = 25; 
k = 10;

IC1 = 0;
IC2 = 2;
eq = diff(y(t),t,2) + (c/m) * diff(y,t,1) + (k/m) * y + 0.0065*y(t)^3
%dsolve(eq == 0, y(0) == 0, subs(diff(y),t,0) == 1)
an1 = dsolve(eq == 0, [y(0) == IC1, subs(diff(y),t,0) == IC2])
ezplot(an1)
grid on