Find a Cauchy-Euler differential equation ax2y'' + bxy' + cy = 0, where a, b, and c are real constants, if it is known that (a) m1 = 3 and m2 = -1 are roots of its auxiliary equation, (b) m1 = i is a complex root of its auxiliary equation.

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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.