Internal problem ID [8837]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1257.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {x \left (x -1\right ) y^{\prime \prime }+\left (\left (a +1\right ) x +b \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 27
dsolve(x*(x-1)*diff(diff(y(x),x),x)+((a+1)*x+b)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1}+\hypergeom \left (\left [b +1, a +b +1\right ], \left [b +2\right ], x\right ) x^{b +1} c_{2} \]
✓ Solution by Mathematica
Time used: 0.064 (sec). Leaf size: 23
DSolve[(b + (1 + a)*x)*y'[x] + (-1 + x)*x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 B_x(b+1,-a-b)+c_2 \\ \end{align*}