Solve the given differential equation xy y 0 This section

Solve the given differential equation.

xy\'\' + y\' = 0

This section is about the Cauchy-Euler method. I couldnt figure out how to do it since the x power is not the same as the power of y which is 2.

Solution

let y\' = v

=>

given equation becomes

xv\' + v = 0

=>

xdv +vdx = 0

=>

d(xv) = 0

=>

xv = c1

=>

xy\' = c1

y\' = c1/x

=>

y = c1*lnx +c2