2.1394   ODE No. 1394

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

$$y^{″}(x)=-\frac{cy(x)}{x^2(ax+b{)}^2}-\frac{2y^{\prime }(x)}{x}$$ ✓ Mathematica : cpu = 0.0501997 (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 = 1.01 (sec), leaf count = 89

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\sqrt{\frac{ax+b}{x}}{\left(\frac{x}{ax+b}\right)}^{\frac{a}{2b}\sqrt{\frac{b^2-4c}{a^2}}}+\mathit{\_}\mathit{C}\mathit{2}\sqrt{\frac{ax+b}{x}}{\left(\frac{x}{ax+b}\right)}^{-\frac{a}{2b}\sqrt{\frac{b^2-4c}{a^2}}}\}$$