76.17.2 problem 11

Internal problem ID [17688]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.7 (Variation of parameters). Problems at page 280
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 10:59:34 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: 0.006 (sec). Leaf size: 24

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

\[ y = \frac {\left (-2 t +3 c_{2} \right ) {\mathrm e}^{-t}}{3}+c_{1} {\mathrm e}^{2 t} \]

✓ Solution by Mathematica

Time used: 0.019 (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]
 

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