solve the DE (diffrential equation)

Question

Solve the DE :

x²y' − 4xy = x⁶ cos(x)

Answer 1

y' - (4/x)y = x⁴cosx.

Integrated factor M = e^∫-4dx/x = e^-4lnx = x^{- 4}.

Multiolaying ODE by M = x^-4. We get x^-4y' - 4x^-3y = cosx;

d/dx(yx^-4) = cosx; yx^-4 = ∫cosxdx; y = x⁴sinx + Cx⁴

Answer 2

dy/dx - 4(y/x) = x⁴cos x

x^-4 is an integrating factor

yx^-4 = ∫cos dx = -sin x + C