linearly independent set of functions

Name Math 264 Summer 2021 Homework Set 3 Show all work! 1. The functions f1 (x) = 5x; f2 (x) = x2 + 3x, and f3 (x) = 2×2 + x do not form a linearly independent set of functions. Verify this by writing one of the given functions as a linear combination of the other two functions. (2 pts.) 2. Show that the functions functions. (2 pts.) ( ) = f1 x e 4x and ( ) = f2 x 2x e form a linearly independent set of 3. Suppose that the auxiliary equation of a fth-order homogeneous linear di erential equation with constant coecients has roots m1 = 1; m2 = 1; m3 = 4; m4 = 2 + i, and m5 = 2 i. What is the solution to the di erential equation? (2 pts.) 1 4. Solve y 000 y 00 9y + 9y = 0. 0 (4 pts.) 5. Use the method of undetermined coecients to solve y 2 00 6y + 8y = 2x + 1 + 4e2x . 0 (5 pts.) 6. Use variation of parameters to solve y 00 4y + 3y = e5x . 0 3 (5 pts.)
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