Internal problem ID [13232]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 6. Laplace transform. Section 6.4. page 608
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+5 y=\delta \left (-3+t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 5.718 (sec). Leaf size: 37
dsolve([diff(y(t),t$2)+2*diff(y(t),t)+5*y(t)=Dirac(t-3),y(0) = 1, D(y)(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{-t} \left (\cos \left (2 t \right )+\sin \left (2 t \right )\right )+\frac {{\mathrm e}^{-t +3} \operatorname {Heaviside}\left (t -3\right ) \sin \left (2 t -6\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.179 (sec). Leaf size: 41
DSolve[{y''[t]+2*y'[t]+5*y[t]==DiracDelta[t-3],{y[0]==1,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} e^{-t} \left (2 (\sin (2 t)+\cos (2 t))-e^3 \theta (t-3) \sin (6-2 t)\right ) \]