Internal problem ID [7161]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 437.
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=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 12
dsolve((1-x)*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x +c_{2} {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 17
DSolve[(1-x)*y''[x]+x*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^x-c_2 x \\ \end{align*}