Internal problem ID [7514]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve((1-x)*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = x c_{1} +c_{2} {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 17
DSolve[(1-x)*y''[x]+x*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^x-c_2 x \]