check if the differential equation x^2 * y’ = x* y + y^2 is:

Question

check if the differential equation x^2 * y’ = x* y + y^2 is:

a) linear

b) separable

c) Exact

Answer 1

This ODE is a first order non-linear ODE (because of the y^(2) term). It is not separable and it is not exact. It belongs to the Bernoulli family of ODEs and it has an exact solution of y=x/(c-lnx).