Exercise · ZW-LAPLACE-TRANSFORM-OF-A-DERIVATIVE-005 · ★★☆ Intermediate
Transforming \(y'+y=1\), \(y(0)=0\), what \(Y(s)\) results?
Choose one option.
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- C. \(\dfrac{1}{s(s+1)}\)
Explanation
We get \(sY+Y=\frac1s\), so \(Y=\frac1{s(s+1)}\). Forgetting \(\mathcal L\{1\}=1/s\) leads to \(\frac1{s+1}\).
Review the concept: Laplace transform of a derivative
The Laplace transform \(\mathcal L\) of the derivative \(f'\) of a function \(f(t)\) with transform \(F(s)\) is an expression in \(F(s)\) and the initial value \(f(0)\).
\[\mathcal L\{f'\}(s)=sF(s)-f(0)\]
More practice problems: laplace transform of a derivative
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