ODE No. 1225

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

✓ Mathematica : cpu = 0.0371588 (sec), leaf count = 39

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

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

✓ Maple : cpu = 0.047 (sec), leaf count = 23

dsolve((x^2+1)*diff(diff(y(x),x),x)-x*diff(y(x),x)+y(x)=0,y(x))

\[y \left (x \right ) = -\sqrt {x^{2}+1}\, c_{2} +x \left (\operatorname {arcsinh}\left (x \right ) c_{2} +c_{1} \right )\]