Internal problem ID [9650]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1316.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_elliptic, _class_II]]
\[ \boxed {x \left (x^{2}-1\right ) y^{\prime \prime }+\left (x^{2}-1\right ) y^{\prime }-x y=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 18
dsolve(x*(x^2-1)*diff(diff(y(x),x),x)+(x^2-1)*diff(y(x),x)-x*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \operatorname {EllipticE}\left (x \right )+c_{2} \left (\operatorname {EllipticCE}\left (x \right )-\operatorname {EllipticCK}\left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.508 (sec). Leaf size: 38
DSolve[-(x*y[x]) + (-1 + x^2)*y'[x] + x*(-1 + x^2)*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 G_{2,2}^{2,0}\left (x^2| \begin {array}{c} \frac {1}{2},\frac {3}{2} \\ 0,0 \\ \end {array} \right )+\frac {2 c_1 \operatorname {EllipticE}\left (x^2\right )}{\pi } \]