# Does this differential equation have very lengthy solution?

• Jun 25th 2018, 05:13 AM
Vinod
Does this differential equation have very lengthy solution?
Hello,
$\frac{dy}{dx}=\frac{x+1}{y(y+2)}$

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

Integrating both the sides, we get
$\frac{(y^3+3y^2)}{3}=\frac{(x^2+2x)}{2}+c$

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?
• Jun 25th 2018, 05:21 AM
SlipEternal
Re: Does this differential equation have very lengthy solution?
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.