Consider the IVP
for , and , .
I have rewritten this differential equation as a system of first-order ODE's such that
The solution is ,
I am asked to perform one step of Euler's method with , and determine if Euler's method is stable for this problem.
For the first part, I find that one step of Euler's method yields
But how do I determine if Euler's method is stable? I know that for the equation , Euler's method is stable for , but since this problem is in a different form I'm not sure what I need to do here.