Can Euler's Method Solve y'=y/x with Initial Conditions?

[lydia_zhu]

Hi everyone.

I was asked to learn Euler's method by myself but I was really confused with this question. How can I work out this equation by using Eulers' method (which is a method solving first order fifferencial equation with initial conditions)
Given：y'=y/x, y(2)=3, use h=0.2, what is y(2.8) ?

thanks very much!

 

[hunt_mat]

You write
$$\frac{dy}{dx}=\frac{y(x+h)-y(x)}{h}$$
to obtain:
$$\frac{y(x+h)-y(x)}{h}=y(x)/x$$
To obtain:
$$y(x+h)=y(x)+\frac{y(x)h}{x}$$
start with $$y(2)$$ and increment.