Internal problem ID [8871]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1293.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Jacobi]
\[ \boxed {144 x \left (x -1\right ) y^{\prime \prime }+\left (120 x -48\right ) y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 35
dsolve(144*x*(x-1)*diff(diff(y(x),x),x)+(120*x-48)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x^{\frac {1}{3}} \operatorname {LegendreP}\left (-\frac {1}{2}, \frac {2}{3}, \sqrt {1-x}\right )+c_{2} x^{\frac {1}{3}} \operatorname {LegendreQ}\left (-\frac {1}{2}, \frac {2}{3}, \sqrt {1-x}\right ) \]
✓ Solution by Mathematica
Time used: 0.168 (sec). Leaf size: 44
DSolve[y[x] + (-48 + 120*x)*y'[x] + 144*(-1 + x)*x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (-1)^{2/3} c_2 x^{2/3} \operatorname {Hypergeometric2F1}\left (\frac {7}{12},\frac {7}{12},\frac {5}{3},x\right )+c_1 \operatorname {Hypergeometric2F1}\left (-\frac {1}{12},-\frac {1}{12},\frac {1}{3},x\right ) \\ \end{align*}