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.

How do you solve the fallowing ode?

$$ u'=u^2 $$

What I did was:

$$ \frac{du}{dt}=u^2 \rightarrow du=u^2dt\rightarrow\int du=\int u^2dt\rightarrow u=u^2(t+c)\rightarrow u=\frac{1}{t+c} $$

but the correct answer is $$ u=\frac{1}{-t+c} $$ Where was I wrong?

share|improve this question
$u=0$ is also a solution, but it's not an interesting solution. –  Ilya Melamed Feb 21 '12 at 19:19

2 Answers 2

up vote 1 down vote accepted

Here is the correct way to do it:

First, divide by $u^2$ to get


Then integrate both sides to get


Finally, rearranging and letting $c=-d$ yields


as desired.

share|improve this answer
As Ilya mentioned $u=0$ is also a solution. –  chango Feb 21 '12 at 19:28

Use the method of separation of variables:

$$\frac{du}{dt}=u^2\Longrightarrow u^{-2}du=dt,$$ $$\int u^{-2}du=\int dt\Longrightarrow -u^{-1}=t+c_1\Longrightarrow u=\frac{1}{c_1-t}.$$

Remember that $c_1$ can 'absorb' the negative sign.

share|improve this answer

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.