Internal problem ID [8867]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1287.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Jacobi]
Solve \begin {gather*} \boxed {9 x \left (x -1\right ) y^{\prime \prime }+3 \left (2 x -1\right ) y^{\prime }-20 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 27
dsolve(9*x*(x-1)*diff(diff(y(x),x),x)+3*(2*x-1)*diff(y(x),x)-20*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: 0.009 (sec). Leaf size: 48
DSolve[-20*y[x] + 3*(-1 + 2*x)*y'[x] + 9*(-1 + x)*x*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)}{\Gamma \left (\frac {1}{3}\right )} \\ \end{align*}