Internal problem ID [13234]
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: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+3 y=\delta \left (t -1\right )-3 \delta \left (t -4\right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 6.562 (sec). Leaf size: 51
dsolve([diff(y(t),t$2)+2*diff(y(t),t)+3*y(t)=Dirac(t-1)-3*Dirac(t-4),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {3 \sqrt {2}\, \left (\operatorname {Heaviside}\left (t -4\right ) {\mathrm e}^{4-t} \sin \left (\sqrt {2}\, \left (t -4\right )\right )-\frac {\operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{-t +1} \sin \left (\sqrt {2}\, \left (t -1\right )\right )}{3}\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.371 (sec). Leaf size: 53
DSolve[{y''[t]+2*y'[t]+3*y[t]==DiracDelta[t-1]-3*DiracDelta[t-4],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {e^{1-t} \left (\theta (t-1) \sin \left (\sqrt {2} (t-1)\right )-3 e^3 \theta (t-4) \sin \left (\sqrt {2} (t-4)\right )\right )}{\sqrt {2}} \]