Internal problem ID [4951]
Book: ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG,
EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section: Chapter 6. Laplace Transforms. Problem set 6.4, page 230
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y-\left (\delta \left (-\pi +t \right )\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 8, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 23
dsolve([diff(y(t),t$2)+4*y(t)=Dirac(t-Pi),y(0) = 8, D(y)(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = 8 \cos \left (2 t \right )+\frac {\theta \left (-\pi +t \right ) \sin \left (2 t \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 23
DSolve[{y''[t]+4*y[t]==DiracDelta[t-Pi],{y[0]==8,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \theta (t-\pi ) \sin (t) \cos (t)+8 \cos (2 t) \\ \end{align*}