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d²y(t) + 2 dy(t) + 5y(t) dx(t) , y(0-) = 2, dy(t) 
=, x(t) = u(t) dt² dt dt dt t-0
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1 e-t sin t u(t) 2 - 2e– t cos t u(t)
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2e– t cost u(t) + 1 e-t sin t u(t) 2 -
1 e-t cos t u(t - 1) + 2e-t sin t u(t - 1) 2
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Correct Option: C
s²Y(s) – 2s + 2sY(s) – 2 + 5Y(s) = 1
∴ (s² + 2s + 5) Y(s) = 3 + 2s
| ⇒ Y(s) = | ||
| s² + 2s + 5 |
| = | + | ||
| (s + 1)² + 2² | (s + 1)² + 2² |
Inverse Laplace transform given,
| ⇒ 2e– t cost u(t) + | e-t sin t u(t) | |
| 2 |
