ODE No. 149

\[ \left (x^2+1\right ) y'(x)-x \left (x^2+1\right )+x y(x)=0 \] Mathematica : cpu = 0.0224785 (sec), leaf count = 27

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

\[\left \{\left \{y(x)\to \frac {1}{3} \left (x^2+1\right )+\frac {c_1}{\sqrt {x^2+1}}\right \}\right \}\] Maple : cpu = 0.01 (sec), leaf count = 20

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

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