Question

A function y(t) satisfies the differential equation dy/dt = y^4 - 6y^3 + 5y^2...

Answer 1

part a says "what are constant solutions of the equation" and I was wondering what they meant by constant solution...

Answer 2

what solutions of the form \(y(t)=C\) for constant \(C\) work here? hint: \(y(t)=C\implies \dfrac{dy}{dt}=0\)

Answer 3

so $$0=C^4-6C^3+5C^2=C^2(C^2-6C+5)=C^2(C-1)(C-5)$$