Does this differential equation have very lengthy solution?

Sep 2011
Mumbai (Bombay),Maharashtra,India

Solution: $(y^2+2y)dy=(x+1)dx$

Integrating both the sides, we get

Now here i am stuck. When i put this differential equation in wolfram alpha it gave me very lengthy solution.Now what should i do?
Last edited:
Nov 2010
You forgot the $+C$. Other than that, if you are looking to get $y$ in terms of $x$, it is not possible with a single formula. You have a cubic polynomial in $y$, so when you solve the cubic, you will have three solutions, and those solutions are not "pretty". I recommend stopping when you get to the step you are currently on (after adding the missing $+C$). There is no need to find an explicit formula for $y$. You did your due diligence and simplified it as much as is needed.
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