# Non-linear first order ODE

1. Jul 23, 2011

### estro

I'm trying to solve the following ODE: $$ydx+(\frac {e^x}{y}-1)dy=0$$

I tried to transfer this ODE into exact form but no luck.

Will appreciate any help.

2. Jul 23, 2011

### LCKurtz

Leave the equation as it is and look for an integrating factor that is just a function of x.

3. Jul 23, 2011

### estro

I tried it before:
$$X=y, Y=e^x/y-1$$
$$u'(x)+(\frac {X_y-Y_x}{Y})u(x)=0$$
Thus u=e^x

But $$d/dy(e^xX) \neq d/dx(e^xY)$$

What I'm missing?

4. Jul 23, 2011

### LCKurtz

Are you sure about the sign on that numerator?

5. Jul 23, 2011

### estro

Bellow is formula that I found in my book:
$$u'(x)+(\frac {X_y-Y_x}{Y})u(x)=0$$=
$$u'(x)-u(x)=0$$ => u=e^x

Can't see where is the problem.

6. Jul 23, 2011

### LCKurtz

I told you what was wrong. The numerator should be Yx-Xy.