ODE No. 481

\[ \left (x^2+y(x)^2\right ) y'(x)+x y(x) y'(x)^2+x y(x)=0 \] Mathematica : cpu = 0.0266205 (sec), leaf count = 49

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

\[\left \{\left \{y(x)\to \frac {c_1}{x}\right \},\left \{y(x)\to -\sqrt {-x^2+2 c_1}\right \},\left \{y(x)\to \sqrt {-x^2+2 c_1}\right \}\right \}\] Maple : cpu = 0.037 (sec), leaf count = 35

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

\[y \left (x \right ) = \frac {c_{1}}{x}\]