2.1601   ODE No. 1601

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

$$a{x}^{r}y(x{)}^n+y^{″}(x)=0$$ ✗ Mathematica : cpu = 0.0375863 (sec), leaf count = 0 , could not solve

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

✓ Maple : cpu = 3.185 (sec), leaf count = 184

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