10.9.7 problem 7

Internal problem ID [1309]
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
Date solved : Monday, January 27, 2025 at 04:50:39 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime }+17 y^{\prime }+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

dsolve(4*diff(y(x),x$2)+17*diff(y(x),x)+4*y(x) = 0,y(x), singsol=all)
 

\[ y = c_1 \,{\mathrm e}^{-4 x}+c_2 \,{\mathrm e}^{-\frac {x}{4}} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 24

DSolve[4*D[y[x],{x,2}]+17*D[y[x],x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-4 x} \left (c_1 e^{15 x/4}+c_2\right ) \]