2.248   ODE No. 248

\[ \left (x^2+6 x y(x)+3\right ) y'(x)+3 y(x)^2+2 x y(x)+2 x=0 \]

✓ Mathematica : cpu = 0.120798 (sec), leaf count = 110

DSolve[2*x + 2*x*y[x] + 3*y[x]^2 + (3 + x^2 + 6*x*y[x])*Derivative[1][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to \frac {-x^2-3}{6 x}-\frac {\sqrt {-2 x^3+\frac {1}{6} \left (x^2+3\right )^2+6 c_1 x}}{\sqrt {6} x}\right \},\left \{y(x)\to \frac {-x^2-3}{6 x}+\frac {\sqrt {-2 x^3+\frac {1}{6} \left (x^2+3\right )^2+6 c_1 x}}{\sqrt {6} x}\right \}\right \}\]

✓ Maple : cpu = 0.019 (sec), leaf count = 75

dsolve((6*x*y(x)+x^2+3)*diff(y(x),x)+3*y(x)^2+2*x*y(x)+2*x = 0,y(x))
 

\[y \left (x \right ) = \frac {-x^{2}-3+\sqrt {x^{4}-12 x^{3}-12 x c_{1} +6 x^{2}+9}}{6 x}\]