Internal problem ID [4958]
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: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+5 y^{\prime }+6 y-\operatorname {Heaviside}\left (t -1\right )-\left (\delta \left (t -2\right )\right )=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 68
dsolve([diff(y(t),t$2)+5*diff(y(t),t)+6*y(t)=Heaviside(t-1)+Dirac(t-2),y(0) = 0, D(y)(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{-2 t}-{\mathrm e}^{-3 t}+\frac {\operatorname {Heaviside}\left (t -1\right )}{6}-\frac {\operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{-2 t +2}}{2}+\operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{-2 t +4}+\frac {\operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{-3 t +3}}{3}-\operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{-3 t +6} \]
✓ Solution by Mathematica
Time used: 0.155 (sec). Leaf size: 71
DSolve[{y''[t]+5*y'[t]+6*y[t]==UnitStep[t-1]+DiracDelta[t-2],{y[0]==0,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to {cc} \{ & {cc} e^{-3 t} \left (-1+e^t\right ) & t\leq 1 \\ \frac {1}{6} e^{-3 t} \left (6 e^4 \left (-e^2+e^t\right ) \theta (t-2)+e^{3 t}-3 e^t \left (-2+e^2\right )+2 e^3-6\right ) & \text {True} \\ \\ \\ \\ \\ \end{align*}