Internal problem ID [4960]
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: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }+5 y-25 t +100 \left (\delta \left (-\pi +t \right )\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = -2, y^{\prime }\relax (0) = 5] \end {align*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 27
dsolve([diff(y(t),t$2)+2*diff(y(t),t)+5*y(t)=25*t-100*Dirac(t-Pi),y(0) = -2, D(y)(0) = 5],y(t), singsol=all)
\[ y \relax (t ) = -50 \theta \left (-\pi +t \right ) \sin \left (2 t \right ) {\mathrm e}^{\pi -t}+5 t -2 \]
✓ Solution by Mathematica
Time used: 0.11 (sec). Leaf size: 29
DSolve[{y''[t]+2*y'[t]+5*y[t]==25*t-100*DiracDelta[t-Pi],{y[0]==-2,y'[0]==5}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -50 e^{\pi -t} \theta (t-\pi ) \sin (2 t)+5 t-2 \\ \end{align*}