4.380   ODE No. 1380

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)=-\frac{by\left(x\right)}{x^2{(x-a)}^2}=0}}$$

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

Mathematica: cpu = 0.297038 (sec), leaf count = 132 $$\left\{\{y(x)\to \frac{c_2(x-a{)}^{\frac{1}{2}\sqrt{\frac{a^2-4b}{a^2}}+\frac{1}{2}}{x}^{\frac{1}{2}-\frac{1}{2}\sqrt{\frac{a^2-4b}{a^2}}}}{a\sqrt{\frac{a^2-4b}{a^2}}}+c_1(x-a{)}^{\frac{1}{2}-\frac{1}{2}\sqrt{1-\frac{4b}{a^2}}}{x}^{\frac{1}{2}\sqrt{1-\frac{4b}{a^2}}+\frac{1}{2}}\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 75 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\sqrt{x(a-x)}{\left(\frac{a-x}{x}\right)}^{\frac{1}{2a}\sqrt{a^2-4b}}+\mathit{\_}\mathit{C}\mathit{2}\sqrt{x(a-x)}{\left(\frac{x}{a-x}\right)}^{\frac{1}{2a}\sqrt{a^2-4b}}\}$$