2.1167   ODE No. 1167

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

$$y(x)(a{x}^m+b)+x^2{y}^{″}(x)-x{y}^{\prime }(x)=0$$ ✓ Mathematica : cpu = 0.0824791 (sec), leaf count = 326

$$\left\{\{y(x)\to c_1{m}^{-\frac{2(m-i\sqrt{b-1}m)}{m^2}-\frac{2i\sqrt{b-1}}{m}}{a}^{\frac{m-i\sqrt{b-1}m}{m^2}+\frac{i\sqrt{b-1}}{m}}{\left(x^m\right)}^{\frac{m-i\sqrt{b-1}m}{m^2}+\frac{i\sqrt{b-1}}{m}}\mathrm{\Gamma }(1-\frac{2i\sqrt{b-1}}{m})J_{-\frac{2i\sqrt{b-1}}{m}}\left(\frac{2\sqrt{a}\sqrt{x^m}}{m}\right)+c_2{m}^{\frac{2i\sqrt{b-1}}{m}-\frac{2(m+i\sqrt{b-1}m)}{m^2}}{a}^{\frac{m+i\sqrt{b-1}m}{m^2}-\frac{i\sqrt{b-1}}{m}}{\left(x^m\right)}^{\frac{m+i\sqrt{b-1}m}{m^2}-\frac{i\sqrt{b-1}}{m}}\mathrm{\Gamma }(\frac{2i\sqrt{b-1}}{m}+1)J_{\frac{2i\sqrt{b-1}}{m}}\left(\frac{2\sqrt{a}\sqrt{x^m}}{m}\right)\}\right\}$$

✓ Maple : cpu = 0.03 (sec), leaf count = 63

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}x{\mathit{J}}_{2\frac{\sqrt{1-b}}{m}}\left(2\frac{\sqrt{a}{x}^{m/2}}{m}\right)+\mathit{\_}\mathit{C}\mathit{2}x{\mathit{Y}}_{2\frac{\sqrt{1-b}}{m}}\left(2\frac{\sqrt{a}{x}^{m/2}}{m}\right)\}$$