Internal problem ID [8917]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1338.
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 (6 x -1\right ) y^{\prime }}{3 x \left (x -2\right )}-\frac {y}{3 x^{2} \left (x -2\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 31
dsolve(diff(diff(y(x),x),x) = 1/3/x*(6*x-1)/(x-2)*diff(y(x),x)+1/3/x^2/(x-2)*y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (18 x^{3}-102 x^{2}+187 x \right )+c_{2} x^{\frac {1}{6}} \left (x -2\right )^{\frac {17}{6}} \]
✓ Solution by Mathematica
Time used: 1.518 (sec). Leaf size: 40
DSolve[y''[x] == y[x]/(3*(-2 + x)*x^2) + ((-1 + 6*x)*y'[x])/(3*(-2 + x)*x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \sqrt [6]{x} (2-x)^{17/6}+\frac {3}{935} c_2 x (6 x (3 x-17)+187) \\ \end{align*}