Internal problem ID [8847]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1269.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Jacobi]
\[ \boxed {2 x \left (x -1\right ) y^{\prime \prime }+\left (\left (2 v +5\right ) x -2 v -3\right ) y^{\prime }+\left (v +1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 40
dsolve(2*x*(x-1)*diff(diff(y(x),x),x)+((2*v+5)*x-2*v-3)*diff(y(x),x)+(v+1)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \operatorname {hypergeom}\left (\left [\frac {1}{2}, v +1\right ], \left [\frac {3}{2}+v \right ], x\right )+c_{2} x^{-\frac {1}{2}-v} \operatorname {hypergeom}\left (\left [\frac {1}{2}, -v \right ], \left [-v +\frac {1}{2}\right ], x\right ) \]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 59
DSolve[(1 + v)*y[x] + (-3 - 2*v + (5 + 2*v)*x)*y'[x] + 2*(-1 + x)*x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \operatorname {Hypergeometric2F1}\left (\frac {1}{2},v+1,v+\frac {3}{2},x\right )-i c_2 i^{-2 v} x^{-v-\frac {1}{2}} \operatorname {Hypergeometric2F1}\left (\frac {1}{2},-v,\frac {1}{2}-v,x\right ) \\ \end{align*}