8. Determine the singular points of the DE and classify each as regular or irregular. Express the equation in standard form, identify P(x) and Q(x) and show supporting work for classification. x*(x-5)° y" +4xy' +(x² – 25)y = 0

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A: the given equation is

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Q: Sketch the bifurcation diagram for y = (A– 4t)y (where A is a parameter, as usual). 2

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Roots

The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form of a + bi.