Internal problem ID [13892]
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 (a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=3 \delta \left (-2+t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 5.0 (sec). Leaf size: 10
dsolve([diff(y(t),t)=3*Dirac(t-2),y(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = 3 \operatorname {Heaviside}\left (t -2\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 11
DSolve[{y'[t]==3*DiracDelta[t-2],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 3 \theta (t-2) \]