So I'm in the process of solving the following differential equation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{dy}{dx}=2y^2 +xy^2[/tex]

with initial condition y(0)=1

I worked it out until I got to the following equation:

[tex]y^2 +y =x^2 -4[/tex]

So now my problem is that I can't isolate y as a function of x in order to move on with the problem and determine where the solution attains its minimum value.

I've tried completing the square and I noticed that the RHS(right hand side) is a difference of squares and I expanded that out but I have no clue how to isolate that y. Now I'm tired and desolate, and I'd like to be pointed back on the right direction.

It's frustrating to be thwarted by algebraic manipulations. :(

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Help simplifying a solution to a differential equation

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