Second Order Linear Differential Equations
Evaluating at x 0, we have 4 A B 1 A 5B. Solving this pair of equations, we get A 19 4 and B 3 4, so our solution is (12.13) y 19 4 e x 3 4 e 5x Example 12.4 A function x x t satisfies the differential equation (12.14) x 2x 15x 0 Under what conditions on the values of x at t 2 0 will this function decay to 0 as t ∞? The auxiliary equation r
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