Internal problem ID [6310]
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]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y=6 \,{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=6*exp(x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x} c_{2} +{\mathrm e}^{x} x c_{1} +3 \,{\mathrm e}^{x} x^{2} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 21
DSolve[y''[x]-2*y'[x]+y[x]==6*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x \left (3 x^2+c_2 x+c_1\right ) \]