# differential equation

Name Math 264 Summer 2021 Homework Set 1 Show all work! 1. Consider the differential equation d3 y dx3 + 2x dy dx (a) Is this a linear di erential equation? 4y = x4 ex . (2 pts.) (b) What is the order of the di erential equation? (2 pts.) 2. Verify that y = xe4x is a solution to the di erential equation y 1 00 8y + 16y = 0. 0 (4 pts.) 3. The two-parameter family of functions y = c1 x6 + c2 x2 solves the di erential equation x2 y 7xy + 12y = 0. Solve the initial-value problem consisting of this di erential equation and the initial conditions y (1) = 4 and y (1) = 6. (4 pts.) 00 0 0 4. Solve the di erential equation. (a) dy dx (4 pts. each) = x3 y 3 2 (b) (x + 4) dy 1 y2 dx =0 3

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