Question

Euler's Method in Matlab

How should I put y'=3cos(t)-2y; y(0)=0 in Matlab, we needed to see the approximate and the exact graph of the equation.

As much as possible, I need the whole script to run it and please also specify important notes. Thank you so much.

Answer 1

Required Matlab code with explanatory comments is given below:

f=@(t,y) 3*cos(t)-2*y; %y'=f(t,y) function
h=0.1; %step size
t=0:h:5; %solving over the range [0,5]
y=zeros(size(t)); %initialize
y(1)=0; %taking initial value y(0)=0
for n=1:length(t)-1
    y(n+1)=y(n)+h*(f(t(n),y(n))); %euler iteration
end
plot(t,y) %draw the graph of the solution curve

The resulting plot of the above code is:

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