Internal problem ID [8871]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1291.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Jacobi]
Solve \begin {gather*} \boxed {48 x \left (x -1\right ) y^{\prime \prime }+\left (152 x -40\right ) y^{\prime }+53 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 50
dsolve(48*x*(x-1)*diff(diff(y(x),x),x)+(152*x-40)*diff(y(x),x)+53*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \hypergeom \left (\left [\frac {13}{12}-\frac {\sqrt {10}}{12}, \frac {13}{12}+\frac {\sqrt {10}}{12}\right ], \left [\frac {5}{6}\right ], x\right )+c_{2} x^{\frac {1}{6}} \hypergeom \left (\left [\frac {5}{4}-\frac {\sqrt {10}}{12}, \frac {5}{4}+\frac {\sqrt {10}}{12}\right ], \left [\frac {7}{6}\right ], x\right ) \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 82
DSolve[53*y[x] + (-40 + 152*x)*y'[x] + 48*(-1 + x)*x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt [6]{-1} c_2 \sqrt [6]{x} \, _2F_1\left (\frac {5}{4}-\frac {\sqrt {\frac {5}{2}}}{6},\frac {1}{12} \left (15+\sqrt {10}\right );\frac {7}{6};x\right )+c_1 \, _2F_1\left (\frac {1}{12} \left (13-\sqrt {10}\right ),\frac {1}{12} \left (13+\sqrt {10}\right );\frac {5}{6};x\right ) \\ \end{align*}