2.1016   ODE No. 1016

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

$$y(x)(a{x}^{2c}+b{x}^{c-1})+y^{″}(x)=0$$ ✓ Mathematica : cpu = 0.134655 (sec), leaf count = 312

$$\left\{\{y(x)\to 2^{\frac{c}{2(c+1)}}{c}_1{\left(x^{c+1}\right)}^{\frac{c}{2(c+1)}}{x}^{-c/2}{e}^{-\frac{\sqrt{a}{x}^{c+1}}{\sqrt{-c^2-2c-1}}}U(\frac{\frac{\sqrt{a}cb}{\sqrt{-(c+1{)}^2}}+\frac{\sqrt{a}b}{\sqrt{-(c+1{)}^2}}+ac}{2(ca+a)},\frac{c}{c+1},\frac{2\sqrt{a}{x}^{c+1}}{\sqrt{-c^2-2c-1}})+2^{\frac{c}{2(c+1)}}{c}_2{\left(x^{c+1}\right)}^{\frac{c}{2(c+1)}}{x}^{-c/2}{e}^{-\frac{\sqrt{a}{x}^{c+1}}{\sqrt{-c^2-2c-1}}}{L}_{-\frac{\frac{\sqrt{a}bc}{\sqrt{-(c+1{)}^2}}+\frac{\sqrt{a}b}{\sqrt{-(c+1{)}^2}}+ac}{2(ac+a)}}^{\frac{c}{c+1}-1}\left(\frac{2\sqrt{a}{x}^{c+1}}{\sqrt{-c^2-2c-1}}\right)\}\right\}$$

✓ Maple : cpu = 0.214 (sec), leaf count = 95

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^{-\frac{c}{2}}{\mathit{M}}_{\frac{-ib}{2c+2}\frac{1}{\sqrt{a}},{(2c+2)}^{-1}}\left(\frac{2i{x}^{c+1}}{c+1}\sqrt{a}\right)+\mathit{\_}\mathit{C}\mathit{2}{x}^{-\frac{c}{2}}{\mathit{W}}_{\frac{-ib}{2c+2}\frac{1}{\sqrt{a}},{(2c+2)}^{-1}}\left(\frac{2i{x}^{c+1}}{c+1}\sqrt{a}\right)\}$$