76.13.20 problem 20

Internal problem ID [17602]
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 : 20
Date solved : Tuesday, January 28, 2025 at 10:45:05 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: 0.003 (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: 0.017 (sec). Leaf size: 34

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

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