76.12.15 problem 26

Internal problem ID [17571]
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 4.2 (Theory of second order linear homogeneous equations). Problems at page 226
Problem number : 26
Date solved : Tuesday, January 28, 2025 at 10:44:21 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

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

\[ y = c_{1} {\mathrm e}^{-x}+{\mathrm e}^{2 x} c_{2} \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 22

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

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