Euler's method code

Hello , how can I code this : y'(t)=cos(t + y) y(0)=0 t[0,3] (exact solution y(t)=-t + 2arctan(t)) using Euler's method like the code below?

clc

clear all

close all

h=0.01;

N=100; % number of steps

y(1)=1;

for n=1:N

y(n+1)=y(n)+h*(-6*y(n));

x(n+1)=n*h;

end

plot(x,y)

hold on

x=0:0.01:1;

y=exp(-6*x); % exact solution

plot(x,y)

Answer 1

[Paul]

The code that is posted solves a differential equation of the form

y'(x) = f(x,y), y(0) = y0

and compares it to the exact solution

y(x) = some function of x

over the interval

x [0 1]

As it happens, your problem has the exact same form, with the independent variable being t instead of x and the endpoint of the interval is different.

[Mike Asmanis]

I know that it solves a different equation , i just need to solve my problem using a simillar or the exact code like the one i posted.

[Mike Asmanis]

I'm getting Array indices must be positive integers or logical values.