Internal problem ID [7081]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 352.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Jacobi]
Solve \begin {gather*} \boxed {x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 45
dsolve(x*(1-x)*diff(y(x),x$2)+(1/2+2*x)*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (4 x +1\right )+c_{2} \left (\left (-12 x -3\right ) \ln \left (-\frac {1}{2}+x +\sqrt {\left (x -1\right ) x}\right )+\left (4 x +26\right ) \sqrt {\left (x -1\right ) x}\right ) \]
✓ Solution by Mathematica
Time used: 0.322 (sec). Leaf size: 62
DSolve[x*(1-x)*y''[x]+(1/2+2*x)*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \left (x+\frac {1}{4}\right )+\frac {1}{2} c_2 \left (\sqrt {-((x-1) x)} (2 x+13)-6 (4 x+1) \cot ^{-1}\left (\frac {\sqrt {x}+1}{\sqrt {1-x}}\right )\right ) \\ \end{align*}