Given This ODE:

y' = (y-2) (x^2+y)^5

y(0)=5

A. Show that this problem has one solution that is defined in an open segment that contains 0.

B. Let y(x) be a solution for this problem. Prove that y(x)>2 for every x in I and conclude that y'(x)>0 in I.

Hint: You can use the solution of the problem: y'=(y-2)(x^2+y)^5 , y(x0)=2

Help is needed !

TNX!