# homogeneous fourth-order Cauchy-Euler di erential equation

Name Math 264 Summer 2021 Homework Set 4 Show all work! 1. Suppose m1 = 2; m2 = 5; m3 = 1 + 3i, and m4 = 1 3i are the solutions to the auxiliary equation of a homogeneous fourth-order Cauchy-Euler di erential equation. Write the general solution to the di erential equation. (3 pts.) 2. Solve the di erential equation. 3×2 y 00 8xy + 10y = 0 (5 pts.) 0 1 3. Obtain the rst four nonzero terms of a Taylor series solution, centered at 0, of the initial-value problem y = y 4 2xy , y (0) = 2, y (0) = 1. (5 pts.) 00 0 0 4. Solve the system of di erential equations consisting of the following equations: (D 4)x y =0 (D + 5)y + 8x = 0. 2 (7 pts.)

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