Internal problem ID [13584]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 31. Delta Functions. Additional Exercises. page 572
Problem number: 31.7 (f).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=\delta \left (t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 5
dsolve([diff(y(t),t$2)+y(t)=Dirac(t),y(0) = 0, D(y)(0) = -1],y(t), singsol=all)
\[ y \left (t \right ) = 0 \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 16
DSolve[{y''[t]+y[t]==DiracDelta[t],{y[0]==0,y'[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to (\theta (t)-\theta (0)-1) \sin (t) \]