Internal problem ID [4073]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number: Exercise 20.11, page 220.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 k y^{\prime }-2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 35
dsolve(diff(y(x),x$2)-2*k*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\left (k +\sqrt {k^{2}+2}\right ) x}+c_{2} {\mathrm e}^{\left (k -\sqrt {k^{2}+2}\right ) x} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 44
DSolve[y''[x]-2*k*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{\left (k-\sqrt {k^2+2}\right ) x}+c_2 e^{\left (\sqrt {k^2+2}+k\right ) x} \\ \end{align*}