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Ordinary Differential Equations

Ordinary Differential Equations - Let $05 and y(t be...

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Unformatted text preview: Let $05) and y(t) be solutions of the system of ordinary differential equations m’:ax+by, :t/":c:v+dya where a, b, c, d are constants. Prove that both m and y are solutions of the second order equation ¢" (0 + my (7?) + 36:5 (t) = 0, where A : — (a + d), and Where B : ad — be. Use this to find the (unique) solution of the system :L":4:E—2y, $(O):1, , with initial conditions y’:3:c—y, y(0):2. ...
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