Internal problem ID [8835]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1255.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {x \left (x -1\right ) y^{\prime \prime }+a y^{\prime }-2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve(x*(x-1)*diff(diff(y(x),x),x)+a*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \left (a^{2}+2 a x +2 x^{2}-a -2 x \right ) c_{1}+c_{2} \left (x -1\right )^{-a} \left (x -1\right ) x^{a} x \]
✓ Solution by Mathematica
Time used: 0.253 (sec). Leaf size: 65
DSolve[-2*y[x] + a*y'[x] + (-1 + x)*x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {(x-1) x \left (\frac {c_2 x^a (1-x)^{-a}}{a-a^3}+2 c_1\right )+a^2 c_1+a c_1 (2 x-1)}{a (a+3)+4} \\ \end{align*}