74.11.26 problem 38

Internal problem ID [16276]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 38
Date solved : Tuesday, January 28, 2025 at 09:00:07 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-y^{\prime }-20 y&=-2 \,{\mathrm e}^{t} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 25

dsolve(diff(y(t),t$2)-diff(y(t),t)-20*y(t)=-2*exp(t),y(t), singsol=all)
 

\[ y = \frac {\left (10 c_{2} {\mathrm e}^{9 t}+{\mathrm e}^{5 t}+10 c_{1} \right ) {\mathrm e}^{-4 t}}{10} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 29

DSolve[D[y[t],{t,2}]-D[y[t],t]-20*y[t]==-2*Exp[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {e^t}{10}+c_1 e^{-4 t}+c_2 e^{5 t} \]