# Thread: Solving difficult differential equation

1. ## Solving difficult differential equation

I have the following differential equation which I want to solve for $y$ as a function of $x$

$\frac{\partial y}{\partial x}=\frac{C_{1}\left(C_{5}y+C_{6}\right)^{2}}{C_{2} \left(C_{3}y+C_{4}\right)-C_{7}\left(C_{5}y+C_{6}\right)^{6}}$

where $C_{1},C_{2},C_{3},C_{4},C_{5},C_{6},C_{7}$ are constants.
Can anyone suggest a method for solving this equation.

2. ## Re: Solving difficult differential equation

Hey JulieK.

Since your expression is separable, you will need to integrate the inverse of the RHS with respect to y. You will have a ratio of two polynomials which means you will need to look at a variety of methods like partial fractions, substitutions, logarithm derivatives and so on.

Have you got access to a table of integrals? If not do a google search and take a look.

Hi chiro