2.1780   ODE No. 1780

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

$$-ax-b+y(x{)}^2{y}^{″}(x)+y(x)y^{\prime }(x{)}^2=0$$ ✗ Mathematica : cpu = 20.3733 (sec), leaf count = 0 , could not solve

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

✓ Maple : cpu = 2.125 (sec), leaf count = 156

$$\{-c_2+\frac{b\ln (ax+b)}{a}-\frac{\sqrt{3}({\int }_{}^{\frac{y\left(x\right)}{ax+b}}-\frac{2(-\frac{3{(-\frac{a}{{\mathit{\text{\_g}}}^3{b}^3})}^{\frac{1}{3}}b\tan \left(\mathrm{RootOf}(6b^2(\int \frac{{(-\frac{a}{{\mathit{\text{\_g}}}^3{b}^3})}^{\frac{2}{3}}{\mathit{\text{\_g}}}^2}{{\mathit{\text{\_g}}}^3{a}^2-1}d\mathit{\text{\_g}})+6c_1-2\sqrt{3}\mathit{\text{\_Z}}+\ln \left(\frac{{\tan }^2\left(\mathit{\text{\_Z}}\right)+1}{{\tan }^2\left(\mathit{\text{\_Z}}\right)+2\sqrt{3}\tan \left(\mathit{\text{\_Z}}\right)+3}\right))\right)}{2}+\sqrt{3}(a-\frac{{(-\frac{a}{{\mathit{\text{\_g}}}^3{b}^3})}^{\frac{1}{3}}b}{2})){\mathit{\text{\_g}}}^{2}b}{{\mathit{\text{\_g}}}^3{a}^2-1}d\mathit{\text{\_g}})}{6}=0\}$$