Internal problem ID [8845]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1265.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x -1\right ) \left (-2+x \right ) y^{\prime \prime }-\left (2 x -3\right ) y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 97
dsolve((x-1)*(x-2)*diff(diff(y(x),x),x)-(2*x-3)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \hypergeom \left (\left [\frac {5}{2}-\frac {\sqrt {5}}{2}, \frac {1}{2}-\frac {\sqrt {5}}{2}\right ], \left [-\sqrt {5}+1\right ], \frac {1}{x -1}\right ) \left (x -2\right )^{2} \left (x -1\right )^{\frac {\sqrt {5}}{2}-\frac {1}{2}}+c_{2} \hypergeom \left (\left [\frac {5}{2}+\frac {\sqrt {5}}{2}, \frac {1}{2}+\frac {\sqrt {5}}{2}\right ], \left [\sqrt {5}+1\right ], \frac {1}{x -1}\right ) \left (x -2\right )^{2} \left (x -1\right )^{-\frac {1}{2}-\frac {\sqrt {5}}{2}} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 55
DSolve[y[x] - (-3 + 2*x)*y'[x] + (-2 + x)*(-1 + x)*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (x-2) (x-1) \left (c_1 P_{\frac {1}{2} \left (-1+\sqrt {5}\right )}^2(2 x-3)+c_2 Q_{\frac {1}{2} \left (-1+\sqrt {5}\right )}^2(2 x-3)\right ) \\ \end{align*}