Internal problem ID [4957]
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: 9.
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^{\prime }+5 y-\left (1-\theta \left (-10+t \right )\right ) {\mathrm e}^{t}+{\mathrm e}^{10} \left (\delta \left (-10+t \right )\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.171 (sec). Leaf size: 49
dsolve([diff(y(t),t$2)+4*diff(y(t),t)+5*y(t)=(1-Heaviside(t-10))*exp(t)-exp(10)*Dirac(t-10),y(0) = 0, D(y)(0) = 1],y(t), singsol=all)
\[ y \relax (t ) = -\frac {\left (\left (-{\mathrm e}^{30} \cos \left (t -10\right )+7 \,{\mathrm e}^{30} \sin \left (t -10\right )+{\mathrm e}^{3 t}\right ) \theta \left (t -10\right )+\cos \relax (t )-7 \sin \relax (t )-{\mathrm e}^{3 t}\right ) {\mathrm e}^{-2 t}}{10} \]
✓ Solution by Mathematica
Time used: 0.664 (sec). Leaf size: 86
DSolve[{y''[t]+4*y'[t]+5*y[t]==(1-UnitStep[t-10])*Exp[t]-Exp[10]*DiracDelta[t-10],{y[0]==0,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to {cc} \{ & {cc} \frac {1}{10} e^{-2 t} \left (-\cos (t)+e^{3 t}+10 e^{30} \theta (t-10) \sin (10-t)+7 \sin (t)\right ) & t\leq 10 \\ \frac {1}{10} e^{-2 t} \left (-\cos (t)+e^{30} (\cos (10-t)+7 \sin (10-t))+7 \sin (t)\right ) & \text {True} \\ \\ \\ \\ \\ \end{align*}