In 9–14 use the Laplace transform to solve the
Chapter 7, Problem 14E(choose chapter or problem)
In Problems 9–14 use the Laplace transform to solve the given initial-value problem. Use the table of Laplace transforms in Appendix III as needed.
\(y^{\prime \prime}+y=f(t)\), y(0) = 1, \(y^{\prime}(0)=0\) where \(f(t)=\left\{\begin{array}{lr}
1, & 0 \leq t<\quad / 2 \\
\sin t, & t \geq / 2
\end{array}\right.
\)
Text Transcription:
y^{\prime \prime}+y=f(t)
y^{\prime}(0)=0
f(t)={{array} lr 1, & 0 leq t<quad / 2 sin t, & t geq 2 {array}
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