Find y in terms of x for the equation 2x(dy/dx) + 4y = 8x^2

divide through by 2x to get: dy/dx + 2y/x = 4x         this is now in the form of dy/dx + P(x)y = Q(x)

intergrating factor = exp( integral(P(x)) dx ) = exp( integral(2/x) dx ) = exp( 2 ln(x) ) = x²

therefore d( (x²)y )/dx = 4 x³  ->  (x²)y = integral ( 4x^3 ) dx = x⁴

therefore y = x²