Internal problem ID [8874]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1294.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Jacobi]
Solve \begin {gather*} \boxed {144 x \left (x -1\right ) y^{\prime \prime }+\left (168 x -96\right ) y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 35
dsolve(144*x*(x-1)*diff(diff(y(x),x),x)+(168*x-96)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{\frac {1}{6}} \LegendreP \left (-\frac {1}{2}, \frac {1}{3}, \sqrt {1-x}\right )+c_{2} x^{\frac {1}{6}} \LegendreQ \left (-\frac {1}{2}, \frac {1}{3}, \sqrt {1-x}\right ) \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 44
DSolve[y[x] + (-96 + 168*x)*y'[x] + 144*(-1 + x)*x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \, _2F_1\left (\frac {1}{12},\frac {1}{12};\frac {2}{3};x\right )+\sqrt [3]{-1} c_2 \sqrt [3]{x} \, _2F_1\left (\frac {5}{12},\frac {5}{12};\frac {4}{3};x\right ) \\ \end{align*}