Math Help - 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.

3. Re: Solving difficult differential equation

Hi chiro

Many thanksfor your reply.
I know this can be integrated but this is not very useful for me.
What I want is y as an explicit function of x. What the integration produces is x as a function of y.

4. Re: Solving difficult differential equation

That will depend on the answer you get. If you can't get y = f(x) then you will have to leave it at that.

Also you can still evaluate y as a function of x using implicit differentiation and putting that through a numerical solver with enough accuracy to keep errors below some threshold: this is what is typically done if you have an implicit function (something that doesn't have y = f(x)).