Exercise · ZW-INVERSE-LAPLACE-TRANSFORM-008 · ★★☆ Intermediate
What is \(\mathcal L^{-1}\left\{\dfrac{s+2}{(s+1)(s+3)}\right\}\)?
Choose one option.
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- D. \(\tfrac12\left(e^{-t}+e^{-3t}\right)\)
Explanation
Partial fractions: \(\frac{s+2}{(s+1)(s+3)}=\frac{1/2}{s+1}+\frac{1/2}{s+3}\), and each term inverts to an exponential.
Review the concept: Inverse Laplace transform
The inverse transform \(\mathcal L^{-1}\) of a function \(F(s)\) is the function \(f(t)\), defined for \(t\ge0\), whose Laplace transform is \(F(s)\).
\[f(t)=\mathcal L^{-1}\{F(s)\}\iff \mathcal L\{f\}=F\]
More practice problems: inverse laplace transform
- ZW-INVERSE-LAPLACE-TRANSFORM-001 What is mathcal L^-1\1s-4\?
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- ZW-INVERSE-LAPLACE-TRANSFORM-003 What is mathcal L^-1\(s)/(s^2+9)\?
- ZW-INVERSE-LAPLACE-TRANSFORM-004 What is mathcal L^-1\(6)/(s^4)\?
- ZW-INVERSE-LAPLACE-TRANSFORM-005 What is mathcal L^-1\(1)/(s(s+1))\?
- ZW-INVERSE-LAPLACE-TRANSFORM-006 What is mathcal L^-1\(2s+3)/(s^2+4)\?
- ZW-INVERSE-LAPLACE-TRANSFORM-007 What is mathcal L^-1\(1)/(s^2+2s+5)\?
- ZW-INVERSE-LAPLACE-TRANSFORM-009 The solution of y''-3y'+2y=0, y(0)=1, y'(0)=0 has Y(s)=(s-3)/((s-1)(s-2)). What is y(t)?
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