4.140   ODE No. 1140

$$\boxed{{\displaystyle ax\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+b\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+cy\left(x\right)=0}}$$

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

Mathematica: cpu = 0.049006 (sec), leaf count = 190 $$\left\{\{y(x)\to c_1{a}^{\frac{1}{2}(\frac{b}{a}-1)}{c}^{\frac{1}{2}(1-\frac{b}{a})}{x}^{\frac{1}{2}(1-\frac{b}{a})}\mathrm{\Gamma }\left(\frac{b}{a}\right)J_{\frac{b}{a}-1}\left(\frac{2\sqrt{c}\sqrt{x}}{\sqrt{a}}\right)+c_2{a}^{\frac{1}{2}(1-\frac{b}{a})-\frac{a-b}{a}}{c}^{\frac{a-b}{a}+\frac{1}{2}(\frac{b}{a}-1)}{x}^{\frac{a-b}{a}+\frac{1}{2}(\frac{b}{a}-1)}\mathrm{\Gamma }(2-\frac{b}{a})J_{1-\frac{b}{a}}\left(\frac{2\sqrt{c}\sqrt{x}}{\sqrt{a}}\right)\}\right\}$$

Maple: cpu = 0.015 (sec), leaf count = 77 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^{\frac{a-b}{2a}}{\mathit{J}}_{\frac{-a+b}{a}}\left(2\sqrt{\frac{c}{a}}\sqrt{x}\right)+\mathit{\_}\mathit{C}\mathit{2}{x}^{\frac{a-b}{2a}}{\mathit{Y}}_{\frac{-a+b}{a}}\left(2\sqrt{\frac{c}{a}}\sqrt{x}\right)\}$$