Internal problem ID [684]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, section 3.6, Variation of Parameters. page
190
Problem number: 2.
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 }-2 y-2 \,{\mathrm e}^{-t}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 24
dsolve(diff(y(t),t$2)-diff(y(t),t)-2*y(t) = 2*exp(-t),y(t), singsol=all)
\[ y \relax (t ) = c_{2} {\mathrm e}^{-t}+c_{1} {\mathrm e}^{2 t}-\frac {2 t \,{\mathrm e}^{-t}}{3} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 32
DSolve[y''[t]-y'[t]-2*y[t] == 2*Exp[-t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{9} e^{-t} \left (-6 t+9 c_2 e^{3 t}-2+9 c_1\right ) \\ \end{align*}