74.12.23 problem 23

Internal problem ID [16330]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.4, page 163
Problem number : 23
Date solved : Tuesday, January 28, 2025 at 09:04:53 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {{\mathrm e}^{-3 t}}{t} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 20

dsolve(diff(y(t),t$2)+6*diff(y(t),t)+9*y(t)=1/t*exp(-3*t),y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 24

DSolve[D[y[t],{t,2}]+6*D[y[t],t]+9*y[t]==1/t*Exp[-3*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-3 t} (t \log (t)+(-1+c_2) t+c_1) \]