Internal problem ID [5581]
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: 5(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y-\left (1-x \right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 16
dsolve((1-x)*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=(1-x)^2,y(x), singsol=all)
\[ y \relax (x ) = c_{2} x +c_{1} {\mathrm e}^{x}+x^{2}+1 \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 22
DSolve[(1-x)*y''[x]+x*y'[x]-y[x]==(1-x)^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2+x-c_2 x+c_1 e^x+1 \\ \end{align*}