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In this tutorial we shall solve a differential equation of the form ( x 2 1) y ′ = x y by using the separating the variables method The differential equation of the form is given as ( x 2 1) y ′ = x If n is a multiple of 4 there are only even solutions, so you can divide by 4 and solve for that Finally, if n divided by four gives residue 1, 2 or 3 there must be 1, 2 or 3 odd numbers in the solution and 2, 1 or 0 even numbers The code below uses all this to cut a few corners

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