Unformatted text preview: positive. 6. Find the solution of the following initial value problem, sketch the graph of the solution, and describe its behavior for increasing t: ¨ x2 ˙ x + 5 x = 0 , x ( π/ 2) = 0 , ˙ x ( π/ 2) = 2 . 7. Find the general solution of the following di²erential equation: 2¨ x + 3 ˙ x + x = t 2 + 3 sin t. 8. Find the solution of the following initial value problem: ¨ x + 2 ˙ x + 5 x = 4 et cos 2 t, x (0) = 1 , ˙ x (0) = 0 . 9. Solve the di²erential equation ¨ x + 2 ˙ x + 5 x = b 1 , ≤ t ≤ π/ 2, , t > π/ 2 with the initial conditions x (0) = 0 and ˙ x (0) = 0. Hint: ±rst solve the initial value problem for t ≤ π/ 2; then solve for t > π/ 2, determining the constants in the latter solution by assuming that x and ˙ x are continuous at t = π/ 2. 1...
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 Spring '09
 T.Qian
 Boundary value problem, Lipschitz continuity

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