Internal problem ID [7002]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 271.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 x \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \relax (x ) = c_{1} x +c_{2} \left (\arctan \left (\sqrt {x -1}\right ) x -\sqrt {x -1}\right ) \]
✓ Solution by Mathematica
Time used: 0.068 (sec). Leaf size: 43
DSolve[2*x*(1-x)*y''[x]+x*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt [4]{2} \left (c_1 x-c_2 \sqrt {1-x}+c_2 x \tanh ^{-1}\left (\sqrt {1-x}\right )\right ) \\ \end{align*}