10.7.8 problem 8

Internal problem ID [1256]
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 : 8
Date solved : Monday, January 27, 2025 at 04:48:02 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 26

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

\[ y = c_1 \,{\mathrm e}^{\left (1+\sqrt {3}\right ) x}+c_2 \,{\mathrm e}^{-\left (\sqrt {3}-1\right ) x} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 34

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

\[ y(x)\to e^{x-\sqrt {3} x} \left (c_2 e^{2 \sqrt {3} x}+c_1\right ) \]