2.1382   ODE No. 1382

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

$$y^{″}(x)=\frac{cy(x)}{(x-a{)}^2(x-b{)}^2}$$ ✓ Mathematica : cpu = 0.714018 (sec), leaf count = 154

$$\left\{\{y(x)\to c_1(x-a{)}^{\frac{1}{2}(\sqrt{\frac{4c}{(a-b{)}^2}+1}+1)}(x-b{)}^{\frac{1}{2}(1-\sqrt{\frac{4c}{(a-b{)}^2}+1})}-\frac{c_2(x-a{)}^{\frac{1}{2}-\frac{1}{2}\sqrt{\frac{4c}{(a-b{)}^2}+1}}(x-b{)}^{\frac{1}{2}\sqrt{\frac{4c}{(a-b{)}^2}+1}+\frac{1}{2}}}{(a-b)\sqrt{\frac{4c}{(a-b{)}^2}+1}}\}\right\}$$

✓ Maple : cpu = 0.125 (sec), leaf count = 116

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