2.1709   ODE No. 1709

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

$$2a^{2}y(x{)}^2-(ay(x)-1)y^{\prime }(x)+ay(x)-2b^{2}y(x{)}^3+y(x)y^{″}(x)-y^{\prime }(x{)}^2=0$$ ✗ Mathematica : cpu = 61.7339 (sec), leaf count = 0 , could not solve

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

✓ Maple : cpu = 2.025 (sec), leaf count = 84

$$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{a},[\{\left(\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)-\frac{2b^2{\mathit{\_}\mathit{a}}^3-2a^2{\mathit{\_}\mathit{a}}^2+a\mathit{\_}\mathit{a}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)+{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2-\mathit{\_}\mathit{a}a-\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)}{\mathit{\_}\mathit{a}}=0\},\{\mathit{\_}\mathit{a}=y\left(x\right),\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\},\{x=\int {\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^{-1}\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)=\mathit{\_}\mathit{a}\}])\}$$