I understand that this requires integration by parts.

Find the function (for ) which satisfies the separable differential equation with the initial condition .

I've gotten to the point where

int y^2 dy = int (10+14x)/x dx

left side with y is straight forward, but the right side with x is ugly.

I made u = (10+14x) and dv = 1/x

du = 14 dx and v = ln(x)

after this i got something really ugly that i can't even type.

Please help me.