In a HW assignment, I'm given the ODE
[itex] y' = f(x,y,\epsilon) [/itex]
and that [itex] y = \phi(x,\epsilon) [/itex]is a solution to this equation.
I'm then asked, is [itex]\phi(x,0)[/itex] a solution to the equation
[itex] y' = f(x,y,0) [/itex]
This result is used for the second part of the problem, and in the question I'm told I can just quote a well known theorem to explain why it's true, but I have no idea what theorem that might be. Any ideas, or maybe how to even prove it?