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.
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