ODE No. 540

$$2y(x)y^{\prime }(x{)}^3-y(x)y^{\prime }(x{)}^2+2x{y}^{\prime }(x)-x=0$$ ✓ Mathematica : cpu = 0.0369771 (sec), leaf count = 69

DSolve[-x + 2*x*Derivative[1][y][x] - y[x]*Derivative[1][y][x]^2 + 2*y[x]*Derivative[1][y][x]^3 == 0,y[x],x]
 

$$\{\{y(x)\to \frac{x}{2}+c_1\},\{y(x)\to \frac{(3c_1-2i{x}^{3/2}){}^{2/3}}{2^{2/3}}\},\{y(x)\to \frac{(2i{x}^{3/2}+3c_1){}^{2/3}}{2^{2/3}}\}\}$$ ✓ Maple : cpu = 0.081 (sec), leaf count = 109

dsolve(2*y(x)*diff(y(x),x)^3-y(x)*diff(y(x),x)^2+2*x*diff(y(x),x)-x=0,y(x))
 

$$x+\frac{x{c}_1}{{\left(\frac{-\sqrt{-xy\left(x\right)}+y\left(x\right)}{y\left(x\right)}\right)}^{\frac{2}{3}}{\left(\frac{-x+\sqrt{-xy\left(x\right)}+y\left(x\right)}{y\left(x\right)}\right)}^{\frac{2}{3}}y\left(x\right)}=0$$