2.187   ODE No. 187

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

$$-ay(x{)}^2-b{x}^{2n-2}+x^n{y}^{\prime }(x)=0$$ ✓ Mathematica : cpu = 0.202499 (sec), leaf count = 328

$$\left\{\{y(x)\to -\frac{x^n(\frac{1}{2}\sqrt{a}\sqrt{b}(\sqrt{\frac{(n-1{)}^2}{ab}-4}-\frac{n-1}{\sqrt{a}\sqrt{b}})x^{\frac{1}{2}\sqrt{a}\sqrt{b}(\sqrt{\frac{(n-1{)}^2}{ab}-4}-\frac{n-1}{\sqrt{a}\sqrt{b}})-1}+\frac{1}{2}\sqrt{a}\sqrt{b}{c}_1(-\frac{n-1}{\sqrt{a}\sqrt{b}}-\sqrt{\frac{(n-1{)}^2}{ab}-4})x^{\frac{1}{2}\sqrt{a}\sqrt{b}(-\frac{n-1}{\sqrt{a}\sqrt{b}}-\sqrt{\frac{(n-1{)}^2}{ab}-4})-1})}{a(x^{\frac{1}{2}\sqrt{a}\sqrt{b}(\sqrt{\frac{(n-1{)}^2}{ab}-4}-\frac{n-1}{\sqrt{a}\sqrt{b}})}+c_1{x}^{\frac{1}{2}\sqrt{a}\sqrt{b}(-\frac{n-1}{\sqrt{a}\sqrt{b}}-\sqrt{\frac{(n-1{)}^2}{ab}-4})})}\}\right\}$$ ✓ Maple : cpu = 0.057 (sec), leaf count = 60

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