10.9.2 problem 2

Internal problem ID [1304]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.4 Repeated roots, reduction of order , page 172
Problem number : 2
Date solved : Monday, January 27, 2025 at 04:50:30 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

dsolve(9*diff(y(x),x$2)+6*diff(y(x),x)+y(x) = 0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-\frac {x}{3}} \left (c_2 x +c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 20

DSolve[9*D[y[x],{x,2}]+6*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x/3} (c_2 x+c_1) \]