Originally Posted by

**arbolis** I must do something wrong. I have to solve $\displaystyle f'(t)=t^2f^2(t)$ with the initial condition $\displaystyle f(0)=\frac{1}{2}$.

So I wrote $\displaystyle \frac{df}{dt}=t^2f^2(t) \Leftrightarrow \frac{df}{f^2(t)}=t^2dt \Leftrightarrow \int \frac{df}{f^2(t)dt}=$ $\displaystyle \int t^2 dt \Leftrightarrow -\frac{1}{f(t)}=\frac{x^3}{3}+C \Leftrightarrow f(t)=-\frac{3}{t^3}+C$. I cleary see that $\displaystyle f$ in $\displaystyle 0$ don't exist, so how could it be equal to $\displaystyle \frac{1}{2}$, since whatever value of $\displaystyle C$ won't satisfy the impossible.