Internal problem ID [5944]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 7 THE LAPLACE TRANSFORM. EXERCISES 7.5. Page 315
Problem number: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-3 y-\left (\delta \left (t -2\right )\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 15
dsolve([diff(y(t),t)-3*y(t)=Dirac(t-2),y(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = \theta \left (t -2\right ) {\mathrm e}^{3 t -6} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 17
DSolve[{y'[t]-3*y[t]==DiracDelta[t-2],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{3 t-6} \theta (t-2) \\ \end{align*}