Internal problem ID [6330]
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: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y=2 x} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 18
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=2*x,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x} c_{2} +{\mathrm e}^{x} x c_{1} +2 x +4 \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 26
DSolve[y''[x]+2*y'[x]+y[x]==2*x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (2 e^x (x-2)+c_2 x+c_1\right ) \]