Consider an initial value problem of the form x′′′ + 3x′′ + 3x′ + x = f(t), x(0) = x′(0) = x′′(0) = 0 where f is a bound

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answerhappygod
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Consider an initial value problem of the form x′′′ + 3x′′ + 3x′ + x = f(t), x(0) = x′(0) = x′′(0) = 0 where f is a bound

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Consider an initial value problem of the form x′′′ + 3x′′ + 3x′+ x = f(t), x(0) = x′(0) = x′′(0) = 0 where f is a boundedcontinuous function.
Then Show that x(t) = 1/2∫ t 0 (τ^2e^(−τ) f(t − τ)dτ).
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