73.22.9 problem 31.7 (b)

Internal problem ID [15636]
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)
Date solved : Tuesday, January 28, 2025 at 08:03:27 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }&=\delta \left (t \right ) \end{align*}

Using Laplace method

✓ Solution by Maple

Time used: 9.337 (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: 60.039 (sec). Leaf size: 43

DSolve[D[y[t],{t,2}]+3*D[y[t],t]==DiracDelta[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \int _1^t\left (e^{-3 K[2]} c_1+e^{-3 K[2]} \int _1^{K[2]}\delta (K[1])dK[1]\right )dK[2]+c_2 \]