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

a) It is not linear because of y²

b) It is not separable because right side is not product f(x)g(y)

c) This equation is not exact: (xy + y²)dx + (- x²)dy = 0 and ∂/∂y(xy + y²) ≠ ∂/∂x(- x²)