Internal problem ID [4956]
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: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+3 y^{\prime }+2 y-10 \sin \relax (t )-10 \left (\delta \left (-1+t \right )\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 47
dsolve([diff(y(t),t$2)+3*diff(y(t),t)+2*y(t)=10*(sin(t)+Dirac(t-1)),y(0) = 1, D(y)(0) = -1],y(t), singsol=all)
\[ y \relax (t ) = 10 \theta \left (t -1\right ) {\mathrm e}^{1-t}-10 \theta \left (t -1\right ) {\mathrm e}^{-2 t +2}+\sin \relax (t )-3 \cos \relax (t )-2 \,{\mathrm e}^{-2 t}+6 \,{\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.051 (sec). Leaf size: 45
DSolve[{y''[t]+3*y'[t]+2*y[t]==10*(Sin[t]+DiracDelta[t-1]),{y[0]==1,y'[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-2 t} \left (10 e \left (e^t-e\right ) \theta (t-1)+6 e^t+e^{2 t} (\sin (t)-3 \cos (t))-2\right ) \\ \end{align*}