Substitution Differential Equation

[KillerZ]

Homework Statement

Solve the given initial value problem.

Homework Equations

$$ydx + x(lnx - lny - 1)dy = 0$$

The Attempt at a Solution

I am confused as to what to do as I can't just substitute y=ux or x=vy because they are not homogeneous of the same degree. And I can't use exact because:

$$\frac{\partial M}{\partial y} \neq \frac{\partial N}{\partial x}$$

 

[Dick]

I don't think u=x/y is such a bad start. ln(x)-ln(y)=ln(x/y)=ln(u). I haven't tried to follow it out. But I would definitely start with that.

 

[LCKurtz]

Are you sure it isn't homogeneous? Remember ln(x) - ln(y) = ln(x/y)

 

[KillerZ]

I got it thanks for the help.