Internal problem ID [2346]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 10, The Laplace Transform and Some Elementary Applications. Exercises for 10.4.
page 689
Problem number: Problem 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y^{\prime }-6 y-12+6 \,{\mathrm e}^{t}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 5, y^{\prime }\relax (0) = -3] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 20
dsolve([diff(y(t),t$2)-diff(y(t),t)-6*y(t)=6*(2-exp(t)),y(0) = 5, D(y)(0) = -3],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left (8 \,{\mathrm e}^{5 t}+5 \,{\mathrm e}^{3 t}-10 \,{\mathrm e}^{2 t}+22\right ) {\mathrm e}^{-2 t}}{5} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 28
DSolve[{y''[t]-y'[t]-6*y[t]==6*(2-Exp[t]),{y[0]==5,y'[0]==-3}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {22 e^{-2 t}}{5}+e^t+\frac {8 e^{3 t}}{5}-2 \\ \end{align*}