10.7.3 problem 3

Internal problem ID [1251]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.1 Homogeneous Equations with Constant Coefficients, page 144
Problem number : 3
Date solved : Monday, January 27, 2025 at 04:47:52 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 17

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

\[ y = \left (c_2 \,{\mathrm e}^{\frac {5 x}{6}}+c_1 \right ) {\mathrm e}^{-\frac {x}{3}} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 26

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

\[ y(x)\to e^{-x/3} \left (c_2 e^{5 x/6}+c_1\right ) \]