ODE No. 260

\[ \left (2 x^2 y(x)+x\right ) y'(x)-x^2 y(x)^3+2 x y(x)^2+y(x)=0 \] Mathematica : cpu = 0.130032 (sec), leaf count = 80

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

\[\left \{\left \{y(x)\to \frac {x}{-2 x^2+\frac {\sqrt {4 x+x (-2 \log (x)+c_1)}}{\sqrt {\frac {1}{x^3}}}}\right \},\left \{y(x)\to -\frac {x}{2 x^2+\frac {\sqrt {4 x+x (-2 \log (x)+c_1)}}{\sqrt {\frac {1}{x^3}}}}\right \}\right \}\] Maple : cpu = 0.03 (sec), leaf count = 59

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

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