Internal problem ID [9706]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1378.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+\frac {2 \left (x^{2}-1\right ) y^{\prime }}{x \left (x -1\right )^{2}}+\frac {\left (-2 x^{2}+2 x +2\right ) y}{x^{2} \left (x -1\right )^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 48
dsolve(diff(diff(y(x),x),x) = -2/x*(x^2-1)/(x-1)^2*diff(y(x),x)-(-2*x^2+2*x+2)/x^2/(x-1)^2*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-x c_{2} \left (x -1\right ) \ln \left (x -1\right )+x c_{2} \left (x -1\right ) \ln \left (x \right )+c_{1} x^{2}+\left (-c_{1} -c_{2} \right ) x +\frac {c_{2}}{2}\right ) x}{\left (x -1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.065 (sec). Leaf size: 56
DSolve[y''[x] == -(((2 + 2*x - 2*x^2)*y[x])/((-1 + x)^2*x^2)) - (2*(-1 + x^2)*y'[x])/((-1 + x)^2*x),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {x \left (c_1 x^2-c_1 x-2 c_2 x-2 c_2 (x-1) x \log (1-x)+2 c_2 (x-1) x \log (x)+c_2\right )}{(x-1)^2} \]