Internal problem ID [5712]
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]]
\[ \boxed {y^{\prime \prime }+5 y^{\prime }+6 y=\operatorname {Heaviside}\left (t -1\right )+\delta \left (-2+t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.937 (sec). Leaf size: 59
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)
\[ y \left (t \right ) = -{\mathrm e}^{-3 t}+{\mathrm e}^{-2 t}+\operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{-2 t +4}-\operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{-3 t +6}-\frac {\operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{-2 t +2}}{2}+\frac {\operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{-3 t +3}}{3}+\frac {\operatorname {Heaviside}\left (t -1\right )}{6} \]
✓ Solution by Mathematica
Time used: 0.208 (sec). Leaf size: 80
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]
\[ y(t)\to \frac {1}{6} e^{-3 t} \left (6 e^4 \left (e^t-e^2\right ) \theta (t-2)-\left (\left (e^t+2 e\right ) \left (e-e^t\right )^2 \theta (1-t)\right )+6 e^t+e^{3 t}-3 e^{t+2}+2 e^3-6\right ) \]