Internal problem ID [659]
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: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime }+17 y^{\prime }+4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(4*diff(y(x),x$2)+17*diff(y(x),x)+4*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-\frac {x}{4}}+c_{2} {\mathrm e}^{-4 x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 24
DSolve[4*y''[x]+17*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-4 x} \left (c_1 e^{15 x/4}+c_2\right ) \\ \end{align*}