Internal problem ID [9623]
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]
\[ \boxed {144 x \left (x -1\right ) y^{\prime \prime }+\left (168 x -96\right ) y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.171 (sec). Leaf size: 33
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)
\[ y \left (x \right ) = \left (\operatorname {LegendreQ}\left (-\frac {1}{2}, \frac {1}{3}, \sqrt {1-x}\right ) c_{2} +\operatorname {LegendreP}\left (-\frac {1}{2}, \frac {1}{3}, \sqrt {1-x}\right ) c_{1} \right ) x^{\frac {1}{6}} \]
✓ Solution by Mathematica
Time used: 0.097 (sec). Leaf size: 44
DSolve[y[x] + (-96 + 168*x)*y'[x] + 144*(-1 + x)*x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \operatorname {Hypergeometric2F1}\left (\frac {1}{12},\frac {1}{12},\frac {2}{3},x\right )+\sqrt [3]{-1} c_2 \sqrt [3]{x} \operatorname {Hypergeometric2F1}\left (\frac {5}{12},\frac {5}{12},\frac {4}{3},x\right ) \]