Internal problem ID [13580]
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 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }=\delta \left (t \right )} \]
✓ Solution by Maple
Time used: 0.157 (sec). Leaf size: 22
dsolve(diff(y(t),t$2)+3*diff(y(t),t)=Dirac(t),y(t), singsol=all)
\[ y = \frac {1}{3}+\frac {y^{\prime }\left (0\right )}{3}+y \left (0\right )-\frac {{\mathrm e}^{-3 t} \left (1+y^{\prime }\left (0\right )\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.138 (sec). Leaf size: 27
DSolve[y''[t]+3*y'[t]==DiracDelta[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{3} \left (\theta (t)-e^{-3 t} (\theta (t)+c_1)\right )+c_2 \]