2.246   ODE No. 246

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

✓ Mathematica : cpu = 0.0981638 (sec), leaf count = 80

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

\[\left \{\left \{y(x)\to \frac {1}{6} \left (-4 x-\frac {\sqrt {2} \sqrt {-x^4+3 e^{4 c_1}}}{x}\right )\right \},\left \{y(x)\to \frac {1}{6} \left (-4 x+\frac {\sqrt {2} \sqrt {-x^4+3 e^{4 c_1}}}{x}\right )\right \}\right \}\]

✓ Maple : cpu = 0.09 (sec), leaf count = 63

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

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