Question

5. Consider the differential equation
dy/dt= y − t.
(a) Work out by hand three steps of Euler’s method with step size .25 for the above
equation, with y(1) = 1.

Answer 1

Euler’s method is a method that's used to approximate solutions of initial value problems of the form \(y'=f(t,y), y(t_0)=y_0\).
In each iteration you should apply \(y_{n+1}=y_n+hf(t_n,y_n)\), where h is the step size.
I will help you with the first iteration on the next post.

Answer 2

Before I start, you need to notice that \(f(t,y)=y-t\).

Iteration#1 (\(n=0)\):
In this iteration we have \(y_n=y_0=1, t_n=t_0=1, \) and \(f(t_n,y_n)=f(t_0,y_0)=0.\)
Hence \(y_1=y_0+hf(t_0,y_0)=1+0.25(0)=1\)

Answer 3

You might want to watch this video here http://www.youtube.com/watch?v=4CqaepeaJHA