Internal problem ID [13576]
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: 31.6 (e).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+2 y=4 \delta \left (-1+t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 16
dsolve([diff(y(t),t)+2*y(t)=4*Dirac(t-1),y(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = 4 \operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{2-2 t} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 18
DSolve[{y'[t]+2*y[t]==4*DiracDelta[t-1],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 4 e^{2-2 t} \theta (t-1) \]