Internal problem ID [15228]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.2 Homogeneous differential equations with
constant coefficients. Exercises page 121
Problem number: 438.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }-2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)-2*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{\left (1+\sqrt {3}\right ) x}+c_{2} {\mathrm e}^{-\left (\sqrt {3}-1\right ) x} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 34
DSolve[y''[x]-2*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{x-\sqrt {3} x} \left (c_2 e^{2 \sqrt {3} x}+c_1\right ) \]