Internal problem ID [13903]
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 (e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-16 y=\delta \left (-10+t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 5.656 (sec). Leaf size: 16
dsolve([diff(y(t),t$2)-16*y(t)=Dirac(t-10),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\operatorname {Heaviside}\left (t -10\right ) \sinh \left (-40+4 t \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 31
DSolve[{y''[t]-16*y[t]==DiracDelta[t-10],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{8} e^{-4 (t+10)} \left (e^{8 t}-e^{80}\right ) \theta (t-10) \]