Internal problem ID [1182]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 5 linear second order equations. Section 5.7 Variation of Parameters. Page
262
Problem number: 28.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y-2 \left (x -1\right )^{2} {\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve((x-1)*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=2*(x-1)^2*exp(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} x +{\mathrm e}^{x} c_{1}+x \left (-2+x \right ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 23
DSolve[(x-1)*y''[x]-x*y'[x]+y[x]==2*(x-1)^2*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x ((x-2) x+c_1)-c_2 x \\ \end{align*}