TITLE: Solving the second order differential equation $y''=y'(2y+1)$
QUESTION [1 upvotes]: $$y'' = y'(2y+1)$$
with $y(0)=1$ and $y'(0)=2$.
Could you please help me with the steps for answering this question.
The answer is 
$$y(x)=-\frac{1}{2} \tanh \left( \frac{x}{2}-\arctan (3) \right) -\frac{1}{2}$$

REPLY [0 votes]: Hint
At first, by integrating you will obtain$$y'=y^2+y+C$$so after applying the initial conditions you have$$y'=y^2+y$$
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