Internal problem ID [5951]
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: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }-1-\left (\delta \left (t -2\right )\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 31
dsolve([diff(y(t),t$2)-2*diff(y(t),t)=1+Dirac(t-2),y(0) = 0, D(y)(0) = 1],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left (2 \,{\mathrm e}^{2 t -4}-2\right ) \theta \left (t -2\right )}{4}-\frac {t}{2}+\frac {3 \,{\mathrm e}^{2 t}}{4}-\frac {3}{4} \]
✓ Solution by Mathematica
Time used: 0.163 (sec). Leaf size: 37
DSolve[{y''[t]-2*y'[t]==1+DiracDelta[t-2],{y[0]==0,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{4} \left (\left (2 e^{2 t-4}-2\right ) \theta (t-2)-2 t+3 e^{2 t}-3\right ) \\ \end{align*}