2.1720   ODE No. 1720

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

$$a{y}^{\prime }(x{)}^2+by(x{)}^2{y}^{\prime }(x)+cy(x{)}^4+y(x)y^{″}(x)=0$$ ✗ Mathematica : cpu = 93.5773 (sec), leaf count = 0 , could not solve

DSolve[c*y[x]^4 + b*y[x]^2*Derivative[1][y][x] + a*Derivative[1][y][x]^2 + y[x]*Derivative[2][y][x] == 0, y[x], x]

✓ Maple : cpu = 0.376 (sec), leaf count = 173

$$\{{\int }^{y\left(x\right)}(2a+4){(\tan \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(2\mathit{\_}\mathit{Z}b{\mathit{\_}\mathit{a}}^2-2\ln \left(\mathit{\_}\mathit{a}\right)a\sqrt{4{\mathit{\_}\mathit{a}}^{4}ac-{\mathit{\_}\mathit{a}}^4{b}^2+8c{\mathit{\_}\mathit{a}}^4}-\sqrt{4{\mathit{\_}\mathit{a}}^{4}ac-{\mathit{\_}\mathit{a}}^4{b}^2+8c{\mathit{\_}\mathit{a}}^4}\ln \left(\frac{{\mathit{\_}\mathit{a}}^4({(\tan \left(\mathit{\_}\mathit{Z}\right))}^2+1)(4ca-b^2+8c)}{4a+8}\right)+\mathit{\_}\mathit{C}\mathit{1}\sqrt{4{\mathit{\_}\mathit{a}}^{4}ac-{\mathit{\_}\mathit{a}}^4{b}^2+8c{\mathit{\_}\mathit{a}}^4})\right)\sqrt{{\mathit{\_}\mathit{a}}^4(4a+8)c-{\mathit{\_}\mathit{a}}^4{b}^2}-b{\mathit{\_}\mathit{a}}^2)}^{-1}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$