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?