2.1684   ODE No. 1684

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

$$xy(x)(a-2x^{2}y(x{)}^2+3xy(x))+b+x^2(2xy(x)+9)y^{\prime }(x)+2x^3{y}^{″}(x)=0$$ ✗ Mathematica : cpu = 46.8498 (sec), leaf count = 0 , could not solve

DSolve[b + x*y[x]*(a + 3*x*y[x] - 2*x^2*y[x]^2) + x^2*(9 + 2*x*y[x])*Derivative[1][y][x] + 2*x^3*Derivative[2][y][x] == 0, y[x], x]

✓ Maple : cpu = 1.4 (sec), leaf count = 100

$$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{a}{\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}},[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=\frac{{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2((-2{\mathit{\_}\mathit{a}}^3+{\mathit{\_}\mathit{a}}^2+(a-5)\mathit{\_}\mathit{a}+b)\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)-2\mathit{\_}\mathit{a}-3)}{2}\},\{\mathit{\_}\mathit{a}=xy\left(x\right),\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=-\frac{1}{x(x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+y\left(x\right))}\},\{x={\left({\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}}\right)}^{-1},y\left(x\right)=\mathit{\_}\mathit{a}{\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}}\}])\}$$