8.217   ODE No. 1807

$$\boxed{{\displaystyle 2x^{2}y\left(x\right){(1-x)}^2(1-y\left(x\right))(x-y\left(x\right))\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)-x^2{(1-x)}^2(x-2xy\left(x\right)-2y\left(x\right)+3{\left(y\left(x\right)\right)}^2){\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2-2xy\left(x\right)(1-x)(1-y\left(x\right))(x^2+y\left(x\right)-2xy\left(x\right))\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+bx{(1-y\left(x\right))}^2{(x-y\left(x\right))}^2-c(1-x){\left(y\left(x\right)\right)}^2{(x-y\left(x\right))}^2-dx{\left(y\left(x\right)\right)}^2(1-x){(1-y\left(x\right))}^2+a{\left(y\left(x\right)\right)}^2{(x-y\left(x\right))}^2{(1-y\left(x\right))}^2=0}}$$

1. Problem in Latex
2. Mathematica input
3. Maple input

Mathematica: cpu = 33.961813 (sec), leaf count = 185 $$\text{DSolve}[a(1-y(x){)}^2(x-y(x){)}^{2}y(x{)}^2+bx(1-y(x){)}^2(x-y(x){)}^2-c(1-x)(x-y(x){)}^{2}y(x{)}^2-d(1-x)x(1-y(x){)}^{2}y(x{)}^2+2(1-x{)}^2{x}^2(1-y(x))(x-y(x))y(x)y^{″}(x)-(1-x{)}^2{x}^2(3y(x{)}^2-2xy(x)-2y(x)+x)y^{\prime }(x{)}^2-2(1-x)x(1-y(x))y(x)(x^2-2xy(x)+y(x))y^{\prime }(x)=0,y(x),x]$$

Maple: cpu = 136.267 (sec), leaf count = 0 $$\text{could not solve}$$