Internal problem ID [4671]
Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill
2014
Section: Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. Supplementary
Problems. page 101
Problem number: Problem 11.48.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }+y-x \,{\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)=x*exp(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{x}+{\mathrm e}^{x} c_{1} x +\frac {{\mathrm e}^{x} x^{3}}{6} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 25
DSolve[y''[x]-2*y'[x]+y[x]==x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} e^x \left (x^3+6 c_2 x+6 c_1\right ) \\ \end{align*}