ODE No. 414

$$x^3+x{y}^{\prime }(x{)}^2+y(x)y^{\prime }(x)=0$$ ✓ Mathematica : cpu = 0.129043 (sec), leaf count = 107

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

$$\{\{y(x)\to x^2\text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{1}{5K[2]+\sqrt{K[2{]}^2-4}}dK[2]\mathrm{\&}][{\int }_1^x-\frac{1}{2K[3]}dK[3]+c_1]\},\{y(x)\to x^2\text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{1}{\sqrt{K[4{]}^2-4}-5K[4]}dK[4]\mathrm{\&}][{\int }_1^x\frac{1}{2K[5]}dK[5]+c_1]\}\}$$ ✓ Maple : cpu = 0.177 (sec), leaf count = 269

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

$${\int }_{\mathit{\text{\_b}}}^x\frac{-y\left(x\right)+\sqrt{-4{\mathit{\text{\_a}}}^4+y{\left(x\right)}^2}}{\mathit{\text{\_a}}(5y\left(x\right)-\sqrt{-4{\mathit{\text{\_a}}}^4+y{\left(x\right)}^2})}d\mathit{\text{\_a}}+{\int }_{}^{y\left(x\right)}\frac{-2+(-80\mathit{\text{\_f}}+16\sqrt{-4x^4+{\mathit{\text{\_f}}}^2})\left({\int }_{\mathit{\text{\_b}}}^x\frac{{\mathit{\text{\_a}}}^3}{{(-5\mathit{\text{\_f}}+\sqrt{-4{\mathit{\text{\_a}}}^4+{\mathit{\text{\_f}}}^2})}^2\sqrt{-4{\mathit{\text{\_a}}}^4+{\mathit{\text{\_f}}}^2}}d\mathit{\text{\_a}}\right)}{5\mathit{\text{\_f}}-\sqrt{-4x^4+{\mathit{\text{\_f}}}^2}}d\mathit{\text{\_f}}+c_1=0$$