74.18.24 problem 30

Internal problem ID [16581]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 30
Date solved : Tuesday, January 28, 2025 at 09:11:31 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=-4 \,{\mathrm e}^{-2 t} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

dsolve(diff(y(t),t$2)-3*diff(y(t),t)+2*y(t)=-4*exp(-2*t),y(t), singsol=all)
 

\[ y = \frac {\left (3 \,{\mathrm e}^{4 t} c_{1} +3 c_{2} {\mathrm e}^{3 t}-1\right ) {\mathrm e}^{-2 t}}{3} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 29

DSolve[D[y[t],{t,2}]-3*D[y[t],t]+2*y[t]==-4*Exp[-2*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\frac {e^{-2 t}}{3}+c_1 e^t+c_2 e^{2 t} \]