Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I'am trying to solve $$\frac{\mathrm{dy} }{\mathrm{d} x}= e^{2x+3y}$$

I use the law of exponent to obtain $$\frac{\mathrm{dy} }{\mathrm{d} x}= e^{2x}e^{3y}$$

I send the $dx$ to the other side and integrate both sides after seperating the variables.$$\int \frac{dy}{e^{3y}} = \int(e^{2x})dx$$

I know the right hand side is equal to $\frac{e^{2x}}{2} + c$.How about the left hand side?

share|improve this question
add comment

2 Answers 2

up vote 3 down vote accepted

Same idea as on the "$x$" side. You are integrating $e^{-3y}dy$, and get $\frac{1}{-3}e^{-3y}$. So we end up with $$\frac{1}{-3}e^{-3y}=\frac{1}{2}e^{2x}+C.$$ This can be simplified in various ways. In this case, you can get an explicit formula for $y$ in terms of $x$.

share|improve this answer
add comment

That is $$\int e^{-3y}dy$$ which is equal to $\frac{1}{-3}e^{-3y}$. Note that $a^b=\frac{1}{a^{-b}}$

share|improve this answer
    
Well done! +++++ –  amWhy Mar 1 '13 at 1:03
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.