1. Suppose m = {0,0,0, 1, –5, 4±3i, 4±3i} are roots of an auxiliary equation. Write down the general solution of the corresponding homogeneous linear DE if it is (а) an equation with constant...

Please answer question 1

Extracted text: 1. Suppose m = {0,0,0, 1, –5, 4±3i, 4±3i} are roots of an auxiliary equation. Write down the general solution of the corresponding homogeneous linear DE if it is (а) an equation with constant coefficients, (b) a Cauchy-Euler equation. 2. Use an appropriate method to find the general solution of the following differential equations: (a) y" + 3y' – 2y = -e2" (5 cos 2x + 9 sin 2x) (b) x?y" + 15xy' + 58y = 0 (c) y" – y = 1- e-2r (d) y" – 6y" + 11y' – 6y = e2" (5 – 4x – 32²)