Which method to solve this differential equation? $$x'=(x+t+1)^2$$
I need to solve this differential equation but do not know how. We cannot use separation of variables so my only guess here would be to use an integrating factor but how would I find that?
EDIT:
the official answer is $x(t) = −t − 1 + \tan(t + C)
$
EDIT2:
subsituting $y = x + t +1$ yielding $y'+1 = y^2$ and integrating
$$\int \frac{dy}{y^{2}+1} = \int dt $$
$$ \arctan(y)=t+C$$
$$ \tan(t+C) = y $$
$$ x+t+1=\tan(t+C)$$
$$ x(t) = \tan(t+C) -t-1$$
Which is the answer

Substitute $$x+t+1=u$$ then $$x'+1=u'$$
