# Math Help - How to solve dy/dx=x^2-sqrt(y)

1. ## How to solve dy/dx=x^2-sqrt(y)

How to solve this differential equation dy/dx=x^2-sqrt(y)? Thanks.

2. ## Re: How to solve dy/dx=x^2-sqrt(y)

I only have two ideas, neither one of which is going to be terribly good news. The first idea is to attempt a series solution. Before doing so, you might want to transform the equation thus: let $u=\sqrt{y},$ implying that $u^{2}=y.$ Then $2uu'=y',$ and the DE becomes

$2uu'=x^{2}-u.$

It might be easier to work with the series solution in this format than with the $y$ equation.

The second idea is to solve the DE numerically. You'll need an initial condition to pull that off.

What is the context for this DE? Does it arise from a physical problem?