# Substitution Differential Equation

1. Oct 7, 2009

### KillerZ

1. The problem statement, all variables and given/known data

Solve the given initial value problem.

2. Relevant equations

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

3. 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:

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

2. Oct 7, 2009

### 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.

3. Oct 7, 2009

### LCKurtz

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

4. Oct 8, 2009

### KillerZ

I got it thanks for the help.