ODE No. 704

\[ y'(x)=\frac {2 a x^3 y(x)^2+2 b x^5-y(x)+x y(x) \log (x)}{x (x \log (x)-1)} \] Mathematica : cpu = 7.64759 (sec), leaf count = 66

DSolve[Derivative[1][y][x] == (2*b*x^5 - y[x] + x*Log[x]*y[x] + 2*a*x^3*y[x]^2)/(x*(-1 + x*Log[x])),y[x],x]
 

\[\left \{\left \{y(x)\to \frac {\sqrt {b} x \tan \left (\sqrt {a} \sqrt {b} \int _1^x\frac {2 K[1]^3}{K[1] \log (K[1])-1}dK[1]+\sqrt {a} \sqrt {b} c_1\right )}{\sqrt {a}}\right \}\right \}\] Maple : cpu = 0.072 (sec), leaf count = 38

dsolve(diff(y(x),x) = (y(x)*ln(x)*x-y(x)+2*x^5*b+2*x^3*a*y(x)^2)/(x*ln(x)-1)/x,y(x))
 

\[y \left (x \right ) = \frac {\tan \left (2 \sqrt {a b}\, \left (c_{1}+\int \frac {x^{3}}{x \ln \left (x \right )-1}d x \right )\right ) x \sqrt {a b}}{a}\]