2.1140   ODE No. 1140

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

$$ax{y}^{″}(x)+b{y}^{\prime }(x)+cy(x)=0$$ ✓ Mathematica : cpu = 0.0490494 (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 = 0.021 (sec), leaf count = 77

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