2.1648   ODE No. 1648

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

$$y^{″}(x)-k{x}^{a}y(x{)}^b{y}^{\prime }(x{)}^c=0$$ ✗ Mathematica : cpu = 0.0796613 (sec), leaf count = 0 , could not solve

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

✓ Maple : cpu = 2.064 (sec), leaf count = 413

$$\{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)}^3}{{(a-c+2)}^2}({\mathit{\_}\mathit{a}}^b{(-\frac{(a-c+2)(\mathit{\_}\mathit{a}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)+1)}{\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)(b+c-1)})}^c{b}^{2}k+2{\mathit{\_}\mathit{a}}^b{(-\frac{(a-c+2)(\mathit{\_}\mathit{a}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)+1)}{\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)(b+c-1)})}^{c}bck+{\mathit{\_}\mathit{a}}^b{(-\frac{(a-c+2)(\mathit{\_}\mathit{a}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)+1)}{\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)(b+c-1)})}^c{c}^{2}k-2{\mathit{\_}\mathit{a}}^b{(-\frac{(a-c+2)(\mathit{\_}\mathit{a}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)+1)}{\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)(b+c-1)})}^{c}bk-2{\mathit{\_}\mathit{a}}^b{(-\frac{(a-c+2)(\mathit{\_}\mathit{a}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)+1)}{\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)(b+c-1)})}^{c}ck+{\mathit{\_}\mathit{a}}^b{(-\frac{(a-c+2)(\mathit{\_}\mathit{a}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)+1)}{\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)(b+c-1)})}^{c}k-\mathit{\_}\mathit{a}{a}^2-\mathit{\_}\mathit{a}ab+ac\mathit{\_}\mathit{a}+\mathit{\_}\mathit{a}cb-3a\mathit{\_}\mathit{a}-2b\mathit{\_}\mathit{a}+c\mathit{\_}\mathit{a}-2\mathit{\_}\mathit{a})+\frac{(2a+b-c+3){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2}{a-c+2}\},\{\mathit{\_}\mathit{a}=y\left(x\right)x^{\frac{a-c+2}{b+c-1}},\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=-\frac{a-c+2}{bx\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+x\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)c+ay\left(x\right)-cy\left(x\right)-x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+2y\left(x\right)}{\left(x^{\frac{a-c+2}{b+c-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})(b+c-1)}{a-c+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}}\}])\}$$