Internal problem ID [8185]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 710.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {2 x \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(2*x*(1-x)*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = x c_{1} +c_{2} \left (\arctan \left (\sqrt {x -1}\right ) x -\sqrt {x -1}\right ) \]
✓ Solution by Mathematica
Time used: 0.064 (sec). Leaf size: 43
DSolve[2*x*(1-x)*y''[x]+x*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sqrt [4]{2} \left (c_2 x \text {arctanh}\left (\sqrt {1-x}\right )+c_1 x-c_2 \sqrt {1-x}\right ) \]