ODE No. 929

$$y^{\prime }(x)=\frac{-\frac{1}{32}{x}^{3}y(x{)}^3+\frac{1}{16}{x}^{2}y(x{)}^3+\frac{3}{16}{x}^{2}y(x{)}^2-\frac{1}{2}xy(x{)}^3+\frac{y(x{)}^3}{4}-\frac{1}{4}xy(x{)}^2-\frac{3}{8}xy(x)+\frac{y(x)}{4}+\frac{1}{4}}{xy(x)}$$ ✓ Mathematica : cpu = 0.757207 (sec), leaf count = 683

DSolve[Derivative[1][y][x] == (1/4 + y[x]/4 - (3*x*y[x])/8 - (x*y[x]^2)/4 + (3*x^2*y[x]^2)/16 + y[x]^3/4 - (x*y[x]^3)/2 + (x^2*y[x]^3)/16 - (x^3*y[x]^3)/32)/(x*y[x]),y[x],x]
 

$$\text{Solve}[{\int }_1^{y(x)}(-32\text{RootSum}[{\mathrm{\#}\text{1}}^{3}K[1{]}^3-2{\mathrm{\#}\text{1}}^{2}K[1{]}^3-8K[1{]}^3-6{\mathrm{\#}\text{1}}^{2}K[1{]}^2+8\mathrm{\#}\text{1}K[1{]}^2+12\mathrm{\#}\text{1}K[1]-8K[1]-8\mathrm{\&},\frac{\log (x-\mathrm{\#}\text{1})}{3{\mathrm{\#}\text{1}}^{2}K[1{]}^2-4\mathrm{\#}\text{1}K[1{]}^2-12\mathrm{\#}\text{1}K[1]+8K[1]+12}\mathrm{\&}]K[1]+\frac{32K[1]}{x^{3}K[1{]}^3-2x^{2}K[1{]}^3-8K[1{]}^3-6x^{2}K[1{]}^2+8xK[1{]}^2+12xK[1]-8K[1]-8}-\frac{8\text{RootSum}[{\mathrm{\#}\text{1}}^{3}K[1{]}^3-2{\mathrm{\#}\text{1}}^{2}K[1{]}^3-8K[1{]}^3-6{\mathrm{\#}\text{1}}^{2}K[1{]}^2+8\mathrm{\#}\text{1}K[1{]}^2+12\mathrm{\#}\text{1}K[1]-8K[1]-8\mathrm{\&},\frac{-x\log (x-\mathrm{\#}\text{1}){\mathrm{\#}\text{1}}^{2}K[1{]}^3+20\log (x-\mathrm{\#}\text{1}){\mathrm{\#}\text{1}}^{2}K[1{]}^3+12x\log (x-\mathrm{\#}\text{1})K[1{]}^3+8\log (x-\mathrm{\#}\text{1})K[1{]}^3-18x\log (x-\mathrm{\#}\text{1})\mathrm{\#}\text{1}K[1{]}^3-12\log (x-\mathrm{\#}\text{1})\mathrm{\#}\text{1}K[1{]}^3+2\log (x-\mathrm{\#}\text{1}){\mathrm{\#}\text{1}}^{2}K[1{]}^2+{\mathrm{\#}\text{1}}^{2}K[1{]}^2+36x\log (x-\mathrm{\#}\text{1})K[1{]}^2+4x\log (x-\mathrm{\#}\text{1})\mathrm{\#}\text{1}K[1{]}^2-44\log (x-\mathrm{\#}\text{1})\mathrm{\#}\text{1}K[1{]}^2+18\mathrm{\#}\text{1}K[1{]}^2-12K[1{]}^2-4x\log (x-\mathrm{\#}\text{1})K[1]+8\log (x-\mathrm{\#}\text{1})K[1]-8\log (x-\mathrm{\#}\text{1})\mathrm{\#}\text{1}K[1]-4\mathrm{\#}\text{1}K[1]-36K[1]+8\log (x-\mathrm{\#}\text{1})+4}{x{\mathrm{\#}\text{1}}^{2}K[1{]}^3-20{\mathrm{\#}\text{1}}^{2}K[1{]}^3+112xK[1{]}^3+18x\mathrm{\#}\text{1}K[1{]}^3-112\mathrm{\#}\text{1}K[1{]}^3-8K[1{]}^3-2{\mathrm{\#}\text{1}}^{2}K[1{]}^2-36xK[1{]}^2-4x\mathrm{\#}\text{1}K[1{]}^2+44\mathrm{\#}\text{1}K[1{]}^2+4xK[1]+8\mathrm{\#}\text{1}K[1]-8K[1]-8}\mathrm{\&}]}{K[1]})dK[1]+16y(x{)}^2\text{RootSum}[{\mathrm{\#}\text{1}}^{3}y(x{)}^3-2{\mathrm{\#}\text{1}}^{2}y(x{)}^3-6{\mathrm{\#}\text{1}}^{2}y(x{)}^2+8\mathrm{\#}\text{1}y(x{)}^2+12\mathrm{\#}\text{1}y(x)-8y(x{)}^3-8y(x)-8\mathrm{\&},\frac{\log (x-\mathrm{\#}\text{1})}{3{\mathrm{\#}\text{1}}^{2}y(x{)}^2-4\mathrm{\#}\text{1}y(x{)}^2-12\mathrm{\#}\text{1}y(x)+8y(x)+12}\mathrm{\&}]+\log (x)=c_1,y(x)]$$ ✓ Maple : cpu = 0.037 (sec), leaf count = 42

dsolve(diff(y(x),x) = -1/32/y(x)*(16*x*y(x)^3-8*y(x)^3-8*y(x)+8*x*y(x)^2-2*x^2*y(x)^3-8+12*x*y(x)-6*x^2*y(x)^2+x^3*y(x)^3)/x,y(x))
 

$$y\left(x\right)=\frac{18}{58\mathrm{RootOf}(-324\left({\int }_{}^{\mathit{\text{\_Z}}}\frac{1}{841{\mathit{\text{\_a}}}^3-27\mathit{\text{\_a}}+27}d\mathit{\text{\_a}}\right)-\ln \left(x\right)+12c_1)+9x-6}$$