2.1664   ODE No. 1664

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

$$a{x}^{m}y(x{)}^n+x{y}^{″}(x)+2y^{\prime }(x)=0$$ ✗ Mathematica : cpu = 0.542318 (sec), leaf count = 0 , could not solve

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

✓ Maple : cpu = 3.003 (sec), leaf count = 155

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