Internal problem ID [5557]
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 2.2. THE METHOD OF UNDETERMINED
COEFFICIENTS. Page 67
Problem number: 1(i).
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 }+y-6 \,{\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=6*exp(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{x}+{\mathrm e}^{x} c_{1} x +3 \,{\mathrm e}^{x} x^{2} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 20
DSolve[y''[x]-2*y'[x]+y[x]==6*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x (x (3 x+c_2)+c_1) \\ \end{align*}