2.853   ODE No. 853

\[ y'(x)=\frac {x^3 y(x)^3+6 x^2 y(x)^2+14 x y(x)+2 x+12}{x^2 (x y(x)+x+2)} \]

✓ Mathematica : cpu = 0.121717 (sec), leaf count = 76

DSolve[Derivative[1][y][x] == (12 + 2*x + 14*x*y[x] + 6*x^2*y[x]^2 + x^3*y[x]^3)/(x^2*(2 + x + x*y[x])),y[x],x]
 

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

✓ Maple : cpu = 0.041 (sec), leaf count = 63

dsolve(diff(y(x),x) = 1/x^2*(14*x*y(x)+12+2*x+x^3*y(x)^3+6*y(x)^2*x^2)/(x*y(x)+2+x),y(x))
 

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