Internal problem ID [4955]
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: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime }+24 y^{\prime }+37 y-17 \,{\mathrm e}^{-t}-\left (\delta \left (t -\frac {1}{2}\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: 0.063 (sec). Leaf size: 36
dsolve([4*diff(y(t),t$2)+24*diff(y(t),t)+37*y(t)=17*exp(-t)+Dirac(t-1/2),y(0) = 1, D(y)(0) = 1],y(t), singsol=all)
\[ y \relax (t ) = \frac {{\mathrm e}^{-3 t} \left (\theta \left (t -\frac {1}{2}\right ) {\mathrm e}^{\frac {3}{2}} \sin \left (-\frac {1}{4}+\frac {t}{2}\right )+8 \sin \left (\frac {t}{2}\right )+2 \,{\mathrm e}^{2 t}\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.065 (sec). Leaf size: 63
DSolve[{4*y''[t]+24*y'[t]+27*y[t]==17*Exp[-t]+DiracDelta[t-1/2],{y[0]==1,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{84} e^{-9 t/2} \left (7 e^{3/4} \left (e^{3 t}-e^{3/2}\right ) \theta (2 t-1)+12 \left (-7 e^{3 t}+17 e^{7 t/2}-3\right )\right ) \\ \end{align*}