Internal problem ID [8814]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1234.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }+2=0} \end {gather*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 57
dsolve((x^2-1)*diff(diff(y(x),x),x)+x*diff(y(x),x)+2=0,y(x), singsol=all)
\[ y \relax (x ) = \int -\frac {2 \sqrt {x^{2}-1}\, \ln \left (x +\sqrt {x^{2}-1}\right ) \sqrt {x -1}\, \sqrt {x +1}-c_{1} x^{2}+c_{1}}{\left (x -1\right )^{\frac {3}{2}} \left (x +1\right )^{\frac {3}{2}}}d x +c_{2} \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 31
DSolve[2 + x*y'[x] + (-1 + x^2)*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2-\frac {1}{4} \left (-2 \tanh ^{-1}\left (\frac {x}{\sqrt {x^2-1}}\right )+c_1\right ){}^2 \\ \end{align*}