2.1380   ODE No. 1380

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

$$y^{″}(x)=-\frac{by(x)}{x^2(x-a{)}^2}$$ ✓ Mathematica : cpu = 0.30347 (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 = 0.113 (sec), leaf count = 75

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