\[ y'(x)=\frac {x^4+x^3+x^3 \log (x)+7 x^2 y(x)^2+7 x y(x)^2+y(x)+7 x y(x)^2 \log (x)}{x} \] ✓ Mathematica : cpu = 0.167162 (sec), leaf count = 59
DSolve[Derivative[1][y][x] == (x^3 + x^4 + x^3*Log[x] + y[x] + 7*x*y[x]^2 + 7*x^2*y[x]^2 + 7*x*Log[x]*y[x]^2)/x,y[x],x]
\[\left \{\left \{y(x)\to \frac {x \tan \left (\frac {1}{12} \left (4 \sqrt {7} x^3+3 \sqrt {7} x^2+6 \sqrt {7} x^2 \log (x)+12 \sqrt {7} c_1\right )\right )}{\sqrt {7}}\right \}\right \}\] ✓ Maple : cpu = 0.065 (sec), leaf count = 37
dsolve(diff(y(x),x) = (y(x)+x^3*ln(x)+x^4+x^3+7*x*y(x)^2*ln(x)+7*x^2*y(x)^2+7*x*y(x)^2)/x,y(x))
\[y \left (x \right ) = \frac {\tan \left (\frac {\left (6 x^{2} \ln \left (x \right )+4 x^{3}+3 x^{2}+12 c_{1}\right ) \sqrt {7}}{12}\right ) x \sqrt {7}}{7}\]