Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

This is a homework that I'm having a bit of trouble with:

Find a general solution of:


Of course this should be done using the method of characteristics but I'm having trouble solving the characteristic equations since none of the equations decouple:


Any suggestions?

share|cite|improve this question
Because people have already answered the question you asked, you should simply start a new question with the correction. Otherwise, the answers that were already given for the question you asked will no longer appear to match the question. I edited this question to restore the original wording. It's perfectly fine to ask a second question, there is no limitation of resources or anything like that to worry about. – doraemonpaul Jan 24 '13 at 1:53
up vote 3 down vote accepted

Follow the method in




$\dfrac{du}{dt}=2$ , letting $u(0)=0$ , we have $u=2t$

$\dfrac{dy}{dt}=2y$ , letting $y(0)=y_0$ , we have $y=y_0e^{2t}=y_0e^u$



Let $w=x^2$ ,

Then $\dfrac{dw}{dt}=2x\dfrac{dx}{dt}$




I.F. $=e^{\int\frac{1}{t}dt}=e^{\ln t}=t$







share|cite|improve this answer
How to handle $y_0$ ? Treat it as a constant? Or what? Can somebody help me? – doraemonpaul Jan 20 '13 at 21:26
Actually there was a typo in the original post. It has been updated – rmh52 Jan 23 '13 at 19:33
Thank you about the hint in given by @Fabian, in fact it just treat $y_0$ as a constant. – doraemonpaul Jan 26 '13 at 0:58

Your Answer


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.