find the particular solution y=f(x) given f(0)=6 and dy/dx= y(x^2-x)?

Question

find the particular solution y=f(x) given f(0)=6 and dy/dx= y(x^2-x)?

Answer 1

dy/y = (x^2-x) dx has general solution

ln y = (1/3)x³-(1/2)x²+C

I will leave it to you to evaluate C from the initial condition.