Internal problem ID [4944]
Book: ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG,
EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section: Chapter 6. Laplace Transforms. Problem set 6.3, page 224
Problem number: 21.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+9 y-\left (\left \{\begin {array}{cc} 8 \sin \relax (t ) & 0<t <\pi \\ 0 & \pi <t \end {array}\right .\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.313 (sec). Leaf size: 33
dsolve([diff(y(t),t$2)+9*y(t)=piecewise(0<t and t<Pi,8*sin(t),t>Pi,0),y(0) = 0, D(y)(0) = 4],y(t), singsol=all)
\[ y \relax (t ) = 4 \left (\left \{\begin {array}{cc} \frac {\sin \left (3 t \right )}{3} & t <0 \\ \sin \relax (t ) \left (\cos ^{2}\relax (t )\right ) & t <\pi \\ \frac {\sin \left (3 t \right )}{3} & \pi \le t \end {array}\right .\right ) \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 29
DSolve[{y''[t]+9*y[t]==Piecewise[{{8*Sin[t],0<t<Pi},{0,t>Pi}}],{y[0]==0,y'[0]==4}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to {cc} \{ & {cc} \sin (t)+\sin (3 t) & 0<t\leq \pi \\ \frac {4}{3} \sin (3 t) & \text {True} \\ \\ \\ \\ \\ \end{align*}