74.12.24 problem 24

Internal problem ID [16331]
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 : 24
Date solved : Tuesday, January 28, 2025 at 09:04:54 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&={\mathrm e}^{-3 t} \ln \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 30

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

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

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 36

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

\[ y(t)\to \frac {1}{4} e^{-3 t} \left (-3 t^2+2 t^2 \log (t)+4 c_2 t+4 c_1\right ) \]