Multiple variables in exponent of first order ODE

• Sep 5th 2011, 01:51 PM
cheme
Multiple variables in exponent of first order ODE
The differential equation is stated as:

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

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.
• Sep 5th 2011, 02:17 PM
pickslides
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

$\displaystyle y' = \frac{3x \times e^{x+2y}}{y} = \frac{3x \times e^{x}\times e^{2y}}{y}$
• Sep 5th 2011, 03:31 PM
cheme
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.