ODE No. 787

$$y^{\prime }(x)=\frac{x(2x^4-2x^{2}y(x)+x^2-x-1)}{(x+1)(x^2-y(x))}$$ ✓ Mathematica : cpu = 23.4919 (sec), leaf count = 488

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

$$\text{Solve}[\frac{(2-\frac{x(x^2-x-1)(2x^2-2y(x)+3)}{\sqrt[3]{x^3{(x^2-x-1)}^3}(x^2-y(x))})(\frac{x(x^2-x-1)(2x^2-2y(x)+3)}{\sqrt[3]{x^3{(x^2-x-1)}^3}(x^2-y(x))}+4)((1-\frac{x(x^2-x-1)(2x^2-2y(x)+3)}{2\sqrt[3]{x^3{(x^2-x-1)}^3}(x^2-y(x))})\log \left(\frac{2-\frac{x(x^2-x-1)(2x^2-2y(x)+3)}{\sqrt[3]{x^3{(x^2-x-1)}^3}(x^2-y(x))}}{\sqrt[3]{2}}\right)+(\frac{x(x^2-x-1)(2x^2-2y(x)+3)}{2\sqrt[3]{x^3{(x^2-x-1)}^3}(x^2-y(x))}-1)\log \left(\frac{\frac{x(x^2-x-1)(2x^2-2y(x)+3)}{\sqrt[3]{x^3{(x^2-x-1)}^3}(x^2-y(x))}+4}{\sqrt[3]{2}}\right)-3)}{18\sqrt[3]{2}(-\frac{{(2x^2-2y(x)+3)}^3}{8{(x^2-y(x))}^3}+\frac{3x(x^2-x-1)(2x^2-2y(x)+3)}{2\sqrt[3]{x^3{(x^2-x-1)}^3}(x^2-y(x))}-2)}=\frac{42^{2/3}{\left(x^3{(x^2-x-1)}^3\right)}^{2/3}(x(x^2-3x+3)-3\log (x+1))}{27x^2{(-x^2+x+1)}^2}+c_1,y(x)]$$ ✓ Maple : cpu = 0.994 (sec), leaf count = 191

dsolve(diff(y(x),x) = 1/(x^2-y(x))*x*(-x-1+x^2-2*x^2*y(x)+2*x^4)/(1+x),y(x))
 

$$y\left(x\right)=\frac{4x^2{\mathrm{e}}^{\mathrm{RootOf}(8x^3{\mathrm{e}}^{\mathit{\text{\_Z}}}-24x^2{\mathrm{e}}^{\mathit{\text{\_Z}}}-36x^3+6\ln \left(\frac{2{\mathrm{e}}^{\mathit{\text{\_Z}}}-9}{{(1+x)}^4}\right){\mathrm{e}}^{\mathit{\text{\_Z}}}+18c_1{\mathrm{e}}^{\mathit{\text{\_Z}}}-6\mathit{\text{\_Z}}{\mathrm{e}}^{\mathit{\text{\_Z}}}+24{\mathrm{e}}^{\mathit{\text{\_Z}}}x+108x^2-27\ln \left(\frac{2{\mathrm{e}}^{\mathit{\text{\_Z}}}-9}{{(1+x)}^4}\right)-81c_1+27\mathit{\text{\_Z}}-108x+27)}-18x^2-9}{4{\mathrm{e}}^{\mathrm{RootOf}(8x^3{\mathrm{e}}^{\mathit{\text{\_Z}}}-24x^2{\mathrm{e}}^{\mathit{\text{\_Z}}}-36x^3+6\ln \left(\frac{2{\mathrm{e}}^{\mathit{\text{\_Z}}}-9}{{(1+x)}^4}\right){\mathrm{e}}^{\mathit{\text{\_Z}}}+18c_1{\mathrm{e}}^{\mathit{\text{\_Z}}}-6\mathit{\text{\_Z}}{\mathrm{e}}^{\mathit{\text{\_Z}}}+24{\mathrm{e}}^{\mathit{\text{\_Z}}}x+108x^2-27\ln \left(\frac{2{\mathrm{e}}^{\mathit{\text{\_Z}}}-9}{{(1+x)}^4}\right)-81c_1+27\mathit{\text{\_Z}}-108x+27)}-18}$$