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.
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