Find the general solution of the differential equation

dy/dx = y^4 ( (x+1) / (x-2)(x^2 + 5)) and any other solutions if they exist.

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- Dec 2nd 2009, 01:59 PMgeorgiahelogeneral solution of a differential equation
Find the general solution of the differential equation

dy/dx = y^4 ( (x+1) / (x-2)(x^2 + 5)) and any other solutions if they exist. - Dec 2nd 2009, 08:20 PMmr fantastic
- Dec 5th 2009, 07:20 AMgeorgiahelo
This is where I get stuck, I need a step by step on how to solve the integral of

(x+1)/(x-2)(x^2+5)

It confuses me as to what I do with the top, and the x^2 on the bottom when dealing with partial fractions.can you help? - Dec 5th 2009, 08:30 AMTheEmptySet
Since you have one linear factor and one irreducible quadratic factor with neither factor repeated, the partial fraction decomposition will have the form.

Now multiply both sides by the LCD to get

expand out the left hand side and collect the powers of x to get

Now we want these two polynomials to be equation so we set the coeffients on each power of x equal to get the following system of equations

Solving this system gives