4. (10%) Solve the ODE \( y'' + 4y' - 21y = r(t) \) where \( r(t) = 1 \) for \( 0 < t \leq 2 \) and \( r(t) = 0 \) for \( t > 2 \) or \( t < 0 \), and the initial condition \( y(0) = 0, y'(0) = 0 \).
阿摩線上測驗
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阿摩線上測驗
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4. (10%) Solve the ODE \( y'' + 4y' - 21y = r(t) \) where \( r(t) = 1 \) for \( 0 < t \leq 2 \) and \( r(t) = 0 \) for \( t > 2 \) or \( t < 0 \), and the initial condition \( y(0) = 0, y'(0) = 0 \).