Internal problem ID [7004]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 273.
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 }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 27
dsolve(x*(1-x)*diff(y(x),x$2)+1/3*(1-2*x)*diff(y(x),x)+20/9*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (6 x -5\right ) x^{\frac {2}{3}}+c_{2} \left (6 x -1\right ) \left (x -1\right )^{\frac {2}{3}} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 48
DSolve[x*(1-x)*y''[x]+1/3*(1-2*x)*y'[x]+20/9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 \sqrt [3]{-((x-1) x)} Q_1^{\frac {2}{3}}(2 x-1)+\frac {c_1 x^{2/3} (6 x-5)}{\operatorname {Gamma}\left (\frac {1}{3}\right )} \\ \end{align*}