How to solve differential equations

Solve the following differential equations:

1. x^2.y' = (x-1)y

2.xy' = [√(x^2 + y^2)] + y

(x^2)(dy/dx) = (x-1)(y)

This is a seperable differential equation:

(dy / y) = (x-1)(dx) / (x^2)

∫dy/y = ∫ (x-1)/x^2 dx

∫dy/ y = ∫ 1/x - 1/x^2

ln|y| = ln|x| + 1/x + C

y = e^(ln|x| + 1/x + C)

Ill come back to do number 2 later

the 2nd is separable after the sub y = wx

w + x [ dw / dx ] =[ x √( 1 + w² ) + wx ] / x = w + √ ( 1 + w² )--->

dw / √ ( 1 + w² ) = dx / x