10.10.2 problem 2

Internal problem ID [1334]
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
Date solved : Monday, January 27, 2025 at 04:51:16 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=2 \,{\mathrm e}^{-t} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 24

dsolve(diff(y(t),t$2)-diff(y(t),t)-2*y(t) = 2*exp(-t),y(t), singsol=all)
 

\[ y = \frac {\left (-2 t +3 c_1 \right ) {\mathrm e}^{-t}}{3}+c_2 \,{\mathrm e}^{2 t} \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 32

DSolve[D[y[t],{t,2}]-D[y[t],t]-2*y[t] == 2*Exp[-t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{9} e^{-t} \left (-6 t+9 c_2 e^{3 t}-2+9 c_1\right ) \]