ODE No. 1312

\[ x \left (x^2+1\right ) y''(x)+2 \left (x^2-1\right ) y'(x)-2 x y(x)=0 \]

✓ Mathematica : cpu = 0.0155062 (sec), leaf count = 32

DSolve[-2*x*y[x] + 2*(-1 + x^2)*Derivative[1][y][x] + x*(1 + x^2)*Derivative[2][y][x] == 0,y[x],x]

\[\left \{\left \{y(x)\to \frac {c_1}{x^2+1}+\frac {c_2 x^3}{3 \left (x^2+1\right )}\right \}\right \}\]

✓ Maple : cpu = 0.026 (sec), leaf count = 19

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))

\[y \left (x \right ) = \frac {c_{2} x^{3}+c_{1}}{x^{2}+1}\]