Ordinary Differential Equations Questions and Answers – General Properties of Inverse Laplace Transform

This set of Ordinary Differential Equations Multiple Choice Questions & Answers (MCQs) focuses on “General Properties of Inverse Laplace Transform”.

1. Find the \(L^{-1} (\frac{s+3}{4s^2+9})\).
a) \(\frac{1}{4} cos⁡(\frac{3t}{2})+\frac{1}{2} cos⁡(\frac{3t}{2})\)
b) \(\frac{1}{4} cos⁡(\frac{3t}{4})+\frac{1}{2} sin⁡(\frac{3t}{2})\)
c) \(\frac{1}{2} cos⁡(\frac{3t}{2})+\frac{1}{2} sin⁡(\frac{3t}{2})\)
d) \(\frac{1}{4} cos⁡(\frac{3t}{2})+\frac{1}{2} sin⁡(\frac{3t}{2})\)
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2. Find the \(L^{-1} (\frac{1}{(s+2)^4})\).
a) \(e^{-2t}×3\)
b) ⁡\(e^{-2t}×\frac{t^3}{3}\)
c) \(e^{-2t}×\frac{t^3}{6}\)
d) \(e^{-2t}×\frac{t^2}{6}\)
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3. Find the \(L^{-1} (\frac{s}{(s-1)^7})\).
a) \(e^{-t} \left (\frac{t^6}{5!}+\frac{t^5}{6!}\right )\)
b) \(e^t \left (\frac{t^6}{5!}+\frac{t^5}{6!}\right )\)
c) \(e^t \left (\frac{t^6}{6!}+\frac{t^5}{5!}\right )\)
d) \(e^{-t} \left (\frac{t^6}{6!}+\frac{t^5}{5!}\right )\)
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4. Find the \(L^{-1} (\frac{s}{2s+9+s^2})\).
a) \(e^{-t} \{cos⁡(2\sqrt{2t})-sin⁡(\sqrt{2t})\}\)
b) \(e^{-t} \{cos⁡(2\sqrt{2t})-sin⁡(2\sqrt{2t})\}\)
c) \(e^{-t} \{cos⁡(2\sqrt{2t})-cos(\sqrt{2t})\}\)
d) \(e^{-2t} \{cos⁡(2\sqrt{2t})-sin⁡(2\sqrt{2t})\}\)
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5. Find the \(L^{-1} \left (\frac{(s+1)}{(s+2)(s+3)}\right )\).
a) 2e^-3t-e^-2t
b) 3e^-3t-e^-2t
c) 2e^-3t-3e^-2t
d) 2e^-2t-e^-t
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6. Find the \(L^{-1} \left (\frac{(3s+9)}{(s+1)(s-1)(s-2)}\right )\).
a) e^-t+6e^t+5e^2t
b) e^-t-e^t+5e^2t
c) e^-3t-6e^t+5e^2t
d) e^-t-6e^t+5e^2t
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7. Find the \(L^{-1} (\frac{1}{(s^2+4)(s^2+9)})\).
a) \(\frac{1}{5} \left (\frac{sin⁡(2t)}{2}-\frac{sin⁡(t)}{3}\right )\)
b) \(\frac{1}{5} \left (\frac{sin⁡(2t)}{2}+\frac{sin⁡(3t)}{3}\right )\)
c) \(\frac{1}{5} \left (\frac{sin⁡(t)}{2}-\frac{sin⁡(3t)}{3}\right )\)
d) \(\frac{1}{5} \left (\frac{sin⁡(2t)}{2}-\frac{sin⁡(3t)}{3}\right )\)
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8. Find the \(L^{-1} \left (\frac{s}{(s^2+1)(s^2+2)(s^2+3)}\right )\).
a) \(\frac{1}{2} cos⁡(t)-cos⁡(\sqrt3t)-\frac{1}{2} cos⁡(\sqrt3t)\)
b) \(\frac{1}{2} cos⁡(t)+cos⁡(\sqrt2t)-\frac{1}{2} cos⁡(\sqrt3t)\)
c) \(\frac{1}{2} cos⁡(t)-cos⁡(\sqrt2t)-\frac{1}{2} cos⁡(\sqrt3t)\)
d) \(\frac{1}{2} cos⁡(t)+cos⁡(\sqrt2t)+\frac{1}{2} cos⁡(\sqrt3t)\)
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9. Find the \(L^{-1} \left (\frac{s+1}{(s-1)(s+2)^2}\right )\).
a) \(\frac{2}{7} e^t-\frac{2}{9} e^{-2t}+\frac{1}{3} e^{-2t}×t\)
b) \(\frac{2}{9} e^t-\frac{2}{9} e^{-2t}+\frac{1}{3} e^{-2t}×t\)
c) \(\frac{2}{9} e^t-\frac{2}{9} e^{-3t}+\frac{1}{3} e^{-2t}×t\)
d) \(\frac{2}{9} e^t-\frac{2}{9} e^{-2t}+\frac{1}{3} e^{-2t}\)
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10. The \(L^{-1} \left (\frac{3s+8}{s^2+4s+25}\right )\) is \(e^{-st} (3cos⁡(\sqrt{21}t+\frac{2sin⁡(\sqrt{21}t)}{\sqrt{21}})\). What is the value of s?
a) 0
b) 1
c) 2
d) 3
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Sanfoundry Global Education & Learning Series – Ordinary Differential Equations.

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