Internal problem ID [13231]
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: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+3 y=5 \delta \left (-2+t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 15.422 (sec). Leaf size: 21
dsolve([diff(y(t),t$2)+3*y(t)=5*Dirac(t-2),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {5 \sqrt {3}\, \operatorname {Heaviside}\left (t -2\right ) \sin \left (\sqrt {3}\, \left (t -2\right )\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.288 (sec). Leaf size: 36
DSolve[{y''[t]+3*y[t]==DiracDelta[t-2],{y[0]==2,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {\theta (t-2) \sin \left (\sqrt {3} (t-2)\right )}{\sqrt {3}}+2 \cos \left (\sqrt {3} t\right ) \]