\[ y'(x)=\frac {4 x^6 y(x)^3+2 x^5 y(x)+2 x^5+3 x^4 y(x)^2+\frac {x^3}{2}+\frac {3}{4} x^2 y(x)+\frac {1}{16}}{x^6 \left (4 x^2 y(x)+4 x^2+1\right )} \] ✓ Mathematica : cpu = 0.187675 (sec), leaf count = 106
DSolve[Derivative[1][y][x] == (1/16 + x^3/2 + 2*x^5 + (3*x^2*y[x])/4 + 2*x^5*y[x] + 3*x^4*y[x]^2 + 4*x^6*y[x]^3)/(x^6*(1 + 4*x^2 + 4*x^2*y[x])),y[x],x]
\[\left \{\left \{y(x)\to -\frac {4 x^2+1}{4 x^2}+\frac {1}{64 x^8 \left (\frac {1}{64 x^8}-\frac {1}{x^8 \sqrt {\frac {8192}{x}+c_1}}\right )}\right \},\left \{y(x)\to -\frac {4 x^2+1}{4 x^2}+\frac {1}{64 x^8 \left (\frac {1}{64 x^8}+\frac {1}{x^8 \sqrt {\frac {8192}{x}+c_1}}\right )}\right \}\right \}\] ✓ Maple : cpu = 0.04 (sec), leaf count = 87
dsolve(diff(y(x),x) = 1/16/x^6*(32*x^5*y(x)+8*x^3+32*x^5+64*x^6*y(x)^3+48*x^4*y(x)^2+12*x^2*y(x)+1)/(4*x^2*y(x)+1+4*x^2),y(x))
\[y \left (x \right ) = \frac {4 x^{2}-\sqrt {\frac {x c_{1}+2}{x}}+1}{4 x^{2} \left (\sqrt {\frac {x c_{1}+2}{x}}-1\right )}\]