2.1762   ODE No. 1762

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

$$ay(x)y^{\prime }(x)+bxy(x{)}^3-x{y}^{\prime }(x{)}^2+xy(x)y^{″}(x)=0$$ ✗ Mathematica : cpu = 48.1884 (sec), leaf count = 0 , could not solve

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

✓ Maple : cpu = 1.019 (sec), leaf count = 108

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