76.13.9 problem 9

Internal problem ID [17591]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 10:44:43 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

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

\[ y = \left (c_{1} {\mathrm e}^{\frac {5 x}{6}}+c_{2} \right ) {\mathrm e}^{-\frac {x}{3}} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 26

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

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