ODE No. 1366

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

✓ Mathematica : cpu = 1.01912 (sec), leaf count = 31

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

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

✓ Maple : cpu = 0.016 (sec), leaf count = 17

dsolve(diff(diff(y(x),x),x) = -2/(x^2+1)*x*diff(y(x),x)-1/(x^2+1)^2*y(x),y(x))

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