Internal problem ID [8891]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1312.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {x \left (x^{2}+1\right ) y^{\prime \prime }+2 \left (x^{2}-1\right ) y^{\prime }-2 y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 26
dsolve(x*(x^2+1)*diff(diff(y(x),x),x)+2*(x^2-1)*diff(y(x),x)-2*x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{x^{2}+1}+\frac {c_{2} x^{3}}{x^{2}+1} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 26
DSolve[-2*x*y[x] + 2*(-1 + x^2)*y'[x] + x*(1 + x^2)*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 x^3+3 c_1}{3 x^2+3} \\ \end{align*}