How do i solve non linear DE in matlab

[David Hill]

https://www.mathworks.com/help/symbolic/solve-a-single-differential-equation.html?searchHighlight=differential%20equation&s_tid=srchtitle_differential%20equation_2

[Ashvin Bhat]

It works for xy^5 and xcosy separately but when it is one single equation it doesn't work, it says this

[AndresVar]

you can try using

ySol(t) = dsolve(ode,cond,'implicit',true)

It gives the same solution as in wolfram alpha. It is a separable first order nonlinear ODE.

Also see you can try ode45 to get numerical solution:

Solve nonstiff differential equations — medium order method - MATLAB ode45 (mathworks.com)

[Ashvin Bhat]

I got this, I don't understand how special cases is causing a problem here since its only a DE which has to be solved, analytical constraints maybe reasonable but since we have given a condition for the DE and have no arbitrary constants it shouldn't be a problem. Can you help me out with the ode45 part?

Answer 1

[Abraham Boayue]

%Here is the required ode45 code.

clear variables

close all

xspan = [0 10];

y0 = 1;

[t,y] = ode45(@(x,y)x.*y.^5+x.*cos(y), xspan, y0);

plot(t,y,'linewidth',2.5)

a = title('y(x) from ode45');

set(a,'fontsize',14);

a = ylabel('y');

set(a,'Fontsize',14);

ylim( [0 10]);

grid