74.11.2 problem 14

Internal problem ID [16252]
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 : 14
Date solved : Tuesday, January 28, 2025 at 08:58:43 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=-{\mathrm e}^{-9 t} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 23

dsolve(diff(y(t),t$2)-4*diff(y(t),t)+3*y(t)=-exp(-9*t),y(t), singsol=all)
 

\[ y = {\mathrm e}^{-9 t} \left (c_{1} {\mathrm e}^{10 t}+c_{2} {\mathrm e}^{12 t}-\frac {1}{120}\right ) \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 29

DSolve[D[y[t],{t,2}]-4*D[y[t],t]+3*y[t]==-Exp[-9*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\frac {e^{-9 t}}{120}+c_1 e^t+c_2 e^{3 t} \]