ODE No. 302

\[ \left (x^2 y(x)^2+x\right ) y'(x)+y(x)=0 \] Mathematica : cpu = 0.106127 (sec), leaf count = 70

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

\[\left \{\left \{y(x)\to \frac {c_1 x-\sqrt {x} \sqrt {4+c_1{}^2 x}}{2 x}\right \},\left \{y(x)\to \frac {c_1 x+\sqrt {x} \sqrt {4+c_1{}^2 x}}{2 x}\right \}\right \}\] Maple : cpu = 0.125 (sec), leaf count = 133

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

\[y \left (x \right ) = -\frac {\sqrt {-2 x c_{1} \left (-2 c_{1}-x +\sqrt {x \left (4 c_{1}+x \right )}\right )}}{2 x c_{1}}\]