General solution of $\dot x=(x^2+tx+t^2)/t^2$ Consider the scalar ODE 
$$\dot x = \frac{x^2+tx+t^2}{t^2}$$ 
I am asked to give the "general solution" of this ODE. I understand that this is the set of all solutions to the ODE but how, exactly, do I give an answer?
Given $(t_0,x_0)\in(\mathbb{R}\setminus\{0\}\times\mathbb{R})$ I was able to show that, on some neighbourhood of $t_0$, $$x = t\tan\left(\ln(t/{t_0})-\arctan(y_0t_0)\right)$$ is the solution. Now am I right stating that $]t_0e^{c-\frac{\pi}{2}},t_0e^{c+\frac{\pi}{2}}[$ with $c=\arctan(y_0t_0)$ is the maximum existence interval and the solution is unique on this interval? Or, did I miss some details as $t$ must not be zero?
In the end, how do I give the general solution? Do I include the maximum existence interval for each $(t_0,x_0)$, or what am I meant to answer? 

hint
Put $$x=u t $$
then
$$x'=u+u't $$
the equation becomes
$$u+u't=u^2+u+1$$
or
$$u't=u^2+1$$
$$\frac {u'}{1+u^2}=\frac {1}{t} $$
You can take it.
