Internal problem ID [8910]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1331.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\frac {\left (x -4\right ) y^{\prime }}{2 x \left (-2+x \right )}+\frac {\left (x -3\right ) y}{2 x^{2} \left (-2+x \right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(diff(y(x),x),x) = 1/2/x*(x-4)/(x-2)*diff(y(x),x)-1/2*(x-3)/x^2/(x-2)*y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sqrt {x}+c_{2} \sqrt {x \left (x -2\right )} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 41
DSolve[y''[x] == -1/2*((-3 + x)*y[x])/((-2 + x)*x^2) + ((-4 + x)*y'[x])/(2*(-2 + x)*x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt [4]{x-2} \sqrt {x} \left (2 c_2 \sqrt {x-2}+c_1\right )}{\sqrt [4]{2-x}} \\ \end{align*}