3.187   ODE No. 187

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

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

Mathematica: cpu = 0.070009 (sec), leaf count = 328 $$\left\{\{y(x)\to -\frac{x^n(\frac{1}{2}\sqrt{a}\sqrt{b}{c}_1(-\frac{n-1}{\sqrt{a}\sqrt{b}}-\sqrt{\frac{(n-1{)}^2}{ab}-4})x^{\frac{1}{2}\sqrt{a}\sqrt{b}(-\frac{n-1}{\sqrt{a}\sqrt{b}}-\sqrt{\frac{(n-1{)}^2}{ab}-4})-1}+\frac{1}{2}\sqrt{a}\sqrt{b}(\sqrt{\frac{(n-1{)}^2}{ab}-4}-\frac{n-1}{\sqrt{a}\sqrt{b}})x^{\frac{1}{2}\sqrt{a}\sqrt{b}(\sqrt{\frac{(n-1{)}^2}{ab}-4}-\frac{n-1}{\sqrt{a}\sqrt{b}})-1})}{a(c_1{x}^{\frac{1}{2}\sqrt{a}\sqrt{b}(-\frac{n-1}{\sqrt{a}\sqrt{b}}-\sqrt{\frac{(n-1{)}^2}{ab}-4})}+x^{\frac{1}{2}\sqrt{a}\sqrt{b}(\sqrt{\frac{(n-1{)}^2}{ab}-4}-\frac{n-1}{\sqrt{a}\sqrt{b}})})}\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 88 $$\{y\left(x\right)=\frac{1}{2a}(-x^{n-1}\tan (-\frac{\ln \left(x\right)}{2}\sqrt{4ab-n^2+2n-1}+\frac{\mathit{\_}\mathit{C}\mathit{1}}{2}\sqrt{4ab-n^2+2n-1})\sqrt{4ab-n^2+2n-1}+x^{n-1}n-x^{n-1})\}$$