4.394   ODE No. 1394

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

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

Mathematica: cpu = 0.050506 (sec), leaf count = 115 $$\left\{\{y(x)\to c_1\exp \left(\frac{\sqrt{c}(-\frac{\sqrt{b^2-4c}}{\sqrt{c}}-\frac{b}{\sqrt{c}})(\log (x)-\log (ax+b))}{2b}\right)+c_2\exp \left(\frac{\sqrt{c}(\frac{\sqrt{b^2-4c}}{\sqrt{c}}-\frac{b}{\sqrt{c}})(\log (x)-\log (ax+b))}{2b}\right)\}\right\}$$

Maple: cpu = 0.078 (sec), leaf count = 89 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\sqrt{\frac{ax+b}{x}}{\left(\frac{x}{ax+b}\right)}^{\frac{a}{2b}\sqrt{\frac{b^2-4c}{a^2}}}+\mathit{\_}\mathit{C}\mathit{2}\sqrt{\frac{ax+b}{x}}{\left(\frac{x}{ax+b}\right)}^{-\frac{a}{2b}\sqrt{\frac{b^2-4c}{a^2}}}\}$$