Exercise · ZW-LAPLACE-TRANSFORM-OF-A-DERIVATIVE-004 · ★☆☆ Basic
Transforming \(y'+2y=0\), \(y(0)=3\), what is \(Y(s)=\mathcal L\{y\}\)?
Choose one option.
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- D. \(\dfrac{3}{s+2}\)
Explanation
We get \(sY-3+2Y=0\), so \((s+2)Y=3\) and \(Y=\frac{3}{s+2}\) (the solution is \(3e^{-2t}\)).
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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