Internal problem ID [5945]
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: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }+y-\left (\delta \left (-1+t \right )\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 18
dsolve([diff(y(t),t)+y(t)=Dirac(t-1),y(0) = 2],y(t), singsol=all)
\[ y \relax (t ) = \theta \left (t -1\right ) {\mathrm e}^{1-t}+2 \,{\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 19
DSolve[{y'[t]+y[t]==DiracDelta[t-1],{y[0]==2}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-t} (e \theta (t-1)+2) \\ \end{align*}