Internal problem ID [13579]
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 (a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+3 y=\delta \left (t -2\right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 22
dsolve([diff(y(t),t)+3*y(t)=Dirac(t-2),y(0) = 2],y(t), singsol=all)
\[ y \left (t \right ) = \operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{6-3 t}+2 \,{\mathrm e}^{-3 t} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 21
DSolve[{y'[t]+3*y[t]==DiracDelta[t-2],{y[0]==2}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-3 t} \left (e^6 \theta (t-2)+2\right ) \]