2.1677   ODE No. 1677

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

$$ay(x)y^{\prime }(x{)}^2+bx+x^2{y}^{″}(x)=0$$ ✗ Mathematica : cpu = 48.006 (sec), leaf count = 0 , could not solve

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

✓ Maple : cpu = 2.275 (sec), leaf count = 101

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