Internal problem ID [6331]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven
Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Second-Order Linear Equations. Section 2.3. THE METHOD OF
VARIATION OF PARAMETERS. Page 71
Problem number: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-y^{\prime }-6 y={\mathrm e}^{-x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)-diff(y(x),x)-6*y(x)=exp(-x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (-4 c_{2} {\mathrm e}^{5 x}+{\mathrm e}^{x}-4 c_{1} \right ) {\mathrm e}^{-2 x}}{4} \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 31
DSolve[y''[x]-y'[x]-6*y[x]==Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {e^{-x}}{4}+c_1 e^{-2 x}+c_2 e^{3 x} \]