ODE No. 148

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

✓ Mathematica : cpu = 0.0335286 (sec), leaf count = 40

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

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

✓ Maple : cpu = 0.011 (sec), leaf count = 16

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

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