10.8.8 problem 14

Internal problem ID [1280]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.3 Complex Roots of the Characteristic Equation , page 164
Problem number : 14
Date solved : Monday, January 27, 2025 at 04:49:34 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 9 y^{\prime \prime }+9 y^{\prime }-4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(9*diff(y(x),x$2) +9*diff(y(x),x)-4*y(x) = 0,y(x), singsol=all)
 

\[ y = \left (c_2 \,{\mathrm e}^{\frac {5 x}{3}}+c_1 \right ) {\mathrm e}^{-\frac {4 x}{3}} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 26

DSolve[9*D[y[x],{x,2}]+9*D[y[x],x]-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-4 x/3} \left (c_2 e^{5 x/3}+c_1\right ) \]