Internal problem ID [654]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {9 y^{\prime \prime }+6 y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(9*diff(y(x),x$2)+6*diff(y(x),x)+y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-\frac {x}{3}}+c_{2} {\mathrm e}^{-\frac {x}{3}} x \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 20
DSolve[9*y''[x]+6*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x/3} (c_2 x+c_1) \\ \end{align*}