Internal problem ID [9666]
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]]
\[ \boxed {y^{\prime \prime }-\frac {\left (6 x -1\right ) y^{\prime }}{3 x \left (x -2\right )}-\frac {y}{3 x^{2} \left (x -2\right )}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
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)
\[ y \left (x \right ) = c_{1} x \left (18 x^{2}-102 x +187\right )+c_{2} \left (x -2\right )^{\frac {17}{6}} x^{\frac {1}{6}} \]
✓ Solution by Mathematica
Time used: 2.412 (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]
\[ y(x)\to \frac {3}{935} c_2 x \left (18 x^2-102 x+187\right )+c_1 \sqrt [6]{x} (2-x)^{17/6} \]