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 = 0.0523907 (sec), leaf count = 120

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

✓ Maple : cpu = 0.026 (sec), leaf count = 66

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