Internal problem ID [13893]
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 (b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=\delta \left (-2+t \right )-\delta \left (t -4\right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 5.015 (sec). Leaf size: 15
dsolve([diff(y(t),t)=Dirac(t-2)-Dirac(t-4),y(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = -\operatorname {Heaviside}\left (t -4\right )+\operatorname {Heaviside}\left (t -2\right ) \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 16
DSolve[{y'[t]==DiracDelta[t-2]-DiracDelta[t-4],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \theta (t-2)-\theta (t-4) \]