Multiple variables in exponent of first order ODE

The differential equation is stated as:

y'=3x exp (x+2y)/y

I have two questions about this problem. First, I am interpreting this problem as follows:

y'=3x^[(x+2y)/y]

Is that correct? If so, that leads me to my second question. Am I able make any substitutions to simply that exponent? It seems as if the substitutions are too complicated thereby making my substituted terms dy and dx extremely complex.

I am not sure how to proceed.

Re: Multiple variables in exponent of first order ODE

Quote:

Originally Posted by

**cheme** The differential equation is stated as:

y'=3x exp (x+2y)/y

$\displaystyle y' = \frac{3x \times e^{x+2y}}{y} = \frac{3x \times e^{x}\times e^{2y}}{y}$

Re: Multiple variables in exponent of first order ODE

Quote:

Originally Posted by

**pickslides** $\displaystyle y' = \frac{3x \times e^{x+2y}}{y} = \frac{3x \times e^{x}\times e^{2y}}{y}$

Thank you. That was my issue with this problem.