How to solve a second order non-homogeneous equation using Euler's approximation

I'm able to approximate a the following homogenous differential equation n''+n'+2n=0, n(0)=5, n'(0)=1 using:

%Defining functions
first=@(n,x,t) x;
second=@(n,x,t) -x-2*n;
%step size
T=.05;
%max t value
tf=10;
%Initial conditions
t(1)=0;
n(1)=5;
n2(1)=1;
%euler approximation
for i=1:(tf/T)
    t(i+1)=t(i)+T;
    n(i+1)=n(i)+T*first(n(i),n2(i)+t(i));
    n2(i+1)=n2(i)+T*second(n(i),n2(i)+t(i));
end
plot(t,n)

However, how should I edit the code above to solve a non-homogenous variation n''+n'+2n=cos(t), with the same initial conditions? Thank you.

Answer 1

[Ameer Hamza]

First, there is a mistake in your equation of Euler method

n(i+1)=n(i)+T*first(n(i),n2(i),t(i)); % there should be a comma between n2(i) and t(i)
n2(i+1)=n2(i)+T*second(n(i),n2(i),t(i)); % there should be a comma between n2(i) and t(i)

You can use cos(t) as input by changing the function 'second'

second=@(n,x,t) -x-2*n+cos(t);