Internal problem ID [5622]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Problems for Review and Discovery. Drill excercises. Page 105
Problem number: 1(e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }-5 y-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)-2*diff(y(x),x)-5*y(x)=x,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\left (1+\sqrt {6}\right ) x} c_{2}+{\mathrm e}^{-\left (-1+\sqrt {6}\right ) x} c_{1}-\frac {x}{5}+\frac {2}{25} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 43
DSolve[y''[x]-2*y'[x]-5*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x}{5}+c_1 e^{x-\sqrt {6} x}+c_2 e^{\left (1+\sqrt {6}\right ) x}+\frac {2}{25} \\ \end{align*}