2.1787   ODE No. 1787

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

$$h(y(x))+2(1-y(x))y(x)y^{″}(x)-(1-3y(x))y^{\prime }(x{)}^2=0$$ ✗ Mathematica : cpu = 100.244 (sec), leaf count = 0 , could not solve

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

✓ Maple : cpu = 0.236 (sec), leaf count = 84

$$\{{\int }^{y\left(x\right)}\frac{1}{\mathit{\_}\mathit{b}-1}\frac{1}{\sqrt{\int \frac{h\left(\mathit{\_}\mathit{b}\right)}{{(\mathit{\_}\mathit{b}-1)}^3{\mathit{\_}\mathit{b}}^2}\mathrm{d}\mathit{\_}\mathit{b}\mathit{\_}\mathit{b}+\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{b}}}d\mathit{\_}\mathit{b}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}-\frac{1}{\mathit{\_}\mathit{b}-1}\frac{1}{\sqrt{\int \frac{h\left(\mathit{\_}\mathit{b}\right)}{{(\mathit{\_}\mathit{b}-1)}^3{\mathit{\_}\mathit{b}}^2}\mathrm{d}\mathit{\_}\mathit{b}\mathit{\_}\mathit{b}+\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{b}}}d\mathit{\_}\mathit{b}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$