# Separation of Variables Help

1. Oct 2, 2006

### prace

http://album6.snapandshare.com/3936/45466/844588.jpg [Broken]

Last edited by a moderator: May 2, 2017
2. Oct 2, 2006

$$\frac{dy}{dx} = e^{3x} \times e^{2y}$$ So $$\int \frac{dy}{e^{2y}} = \int e^{3x} dx$$.

Last edited: Oct 2, 2006
3. Oct 2, 2006

### prace

but the original problem had e raised to the 3x + 2y. The only way I know to get rid of that is to take the natural log of both sides right? If you do that, you are left with ln (dy/dx) on the left side. How did you get rid of the natural log there?

Last edited: Oct 2, 2006
4. Oct 2, 2006

By the properties of exponents we know that $$e^{3x+2y} = e^{3x}\times e^{2y}$$. So we can separate variables without taking the natural log of both sides. In general, $$a^{n+m} = a^{n}\times a^{m}$$