ODE No. 913

$$y^{\prime }(x)=\frac{y(x{)}^3+y(x)+y(x{)}^3(-{\log }^3(x))+y(x{)}^3{\log }^2(x)+3y(x{)}^2{\log }^2(x)-2y(x{)}^2\log (x)-3y(x)\log (x)+1}{xy(x)}$$ ✓ Mathematica : cpu = 0.758696 (sec), leaf count = 716

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

$$\text{Solve}[{\int }_1^{y(x)}(2\text{RootSum}[{\mathrm{\#}\text{1}}^{3}K[1{]}^3-{\mathrm{\#}\text{1}}^{2}K[1{]}^3-2K[1{]}^3-3{\mathrm{\#}\text{1}}^{2}K[1{]}^2+2\mathrm{\#}\text{1}K[1{]}^2+3\mathrm{\#}\text{1}K[1]-K[1]-1\mathrm{\&},\frac{\log (\log (x)-\mathrm{\#}\text{1})}{3{\mathrm{\#}\text{1}}^{2}K[1{]}^2-2\mathrm{\#}\text{1}K[1{]}^2-6\mathrm{\#}\text{1}K[1]+2K[1]+3}\mathrm{\&}]K[1]-\frac{K[1]}{{\log }^3(x)K[1{]}^3-{\log }^2(x)K[1{]}^3-2K[1{]}^3-3{\log }^2(x)K[1{]}^2+2\log (x)K[1{]}^2+3\log (x)K[1]-K[1]-1}+\frac{\text{RootSum}[{\mathrm{\#}\text{1}}^{3}K[1{]}^3-{\mathrm{\#}\text{1}}^{2}K[1{]}^3-2K[1{]}^3-3{\mathrm{\#}\text{1}}^{2}K[1{]}^2+2\mathrm{\#}\text{1}K[1{]}^2+3\mathrm{\#}\text{1}K[1]-K[1]-1\mathrm{\&},\frac{-2\log (x)\log (\log (x)-\mathrm{\#}\text{1}){\mathrm{\#}\text{1}}^{2}K[1{]}^3+38\log (\log (x)-\mathrm{\#}\text{1}){\mathrm{\#}\text{1}}^{2}K[1{]}^3+12\log (x)\log (\log (x)-\mathrm{\#}\text{1})K[1{]}^3+4\log (\log (x)-\mathrm{\#}\text{1})K[1{]}^3-36\log (x)\log (\log (x)-\mathrm{\#}\text{1})\mathrm{\#}\text{1}K[1{]}^3-12\log (\log (x)-\mathrm{\#}\text{1})\mathrm{\#}\text{1}K[1{]}^3+2\log (\log (x)-\mathrm{\#}\text{1}){\mathrm{\#}\text{1}}^{2}K[1{]}^2+{\mathrm{\#}\text{1}}^{2}K[1{]}^2+36\log (x)\log (\log (x)-\mathrm{\#}\text{1})K[1{]}^2+4\log (x)\log (\log (x)-\mathrm{\#}\text{1})\mathrm{\#}\text{1}K[1{]}^2-40\log (\log (x)-\mathrm{\#}\text{1})\mathrm{\#}\text{1}K[1{]}^2+18\mathrm{\#}\text{1}K[1{]}^2-6K[1{]}^2-2\log (x)\log (\log (x)-\mathrm{\#}\text{1})K[1]+2\log (\log (x)-\mathrm{\#}\text{1})K[1]-4\log (\log (x)-\mathrm{\#}\text{1})\mathrm{\#}\text{1}K[1]-2\mathrm{\#}\text{1}K[1]-18K[1]+2\log (\log (x)-\mathrm{\#}\text{1})+1}{\log (x){\mathrm{\#}\text{1}}^{2}K[1{]}^3-19{\mathrm{\#}\text{1}}^{2}K[1{]}^3+110\log (x)K[1{]}^3+18\log (x)\mathrm{\#}\text{1}K[1{]}^3-110\mathrm{\#}\text{1}K[1{]}^3-2K[1{]}^3-{\mathrm{\#}\text{1}}^{2}K[1{]}^2-18\log (x)K[1{]}^2-2\log (x)\mathrm{\#}\text{1}K[1{]}^2+20\mathrm{\#}\text{1}K[1{]}^2+\log (x)K[1]+2\mathrm{\#}\text{1}K[1]-K[1]-1}\mathrm{\&}]}{K[1]})dK[1]+y(x{)}^2(-\text{RootSum}[{\mathrm{\#}\text{1}}^{3}y(x{)}^3-{\mathrm{\#}\text{1}}^{2}y(x{)}^3-3{\mathrm{\#}\text{1}}^{2}y(x{)}^2+2\mathrm{\#}\text{1}y(x{)}^2+3\mathrm{\#}\text{1}y(x)-2y(x{)}^3-y(x)-1\mathrm{\&},\frac{\log (\log (x)-\mathrm{\#}\text{1})}{3{\mathrm{\#}\text{1}}^{2}y(x{)}^2-2\mathrm{\#}\text{1}y(x{)}^2-6\mathrm{\#}\text{1}y(x)+2y(x)+3}\mathrm{\&}])-\log (x)=c_1,y(x)]$$ ✓ Maple : cpu = 0.189 (sec), leaf count = 43

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

$$y\left(x\right)=\frac{9}{9\ln \left(x\right)+56\mathrm{RootOf}(-81\left({\int }_{}^{\mathit{\text{\_Z}}}\frac{1}{3136{\mathit{\text{\_a}}}^3-27\mathit{\text{\_a}}+27}d\mathit{\text{\_a}}\right)-\ln \left(x\right)+3c_1)-3}$$