#### 2.187   ODE No. 187

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

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

$\left \{ y \left ( x \right ) ={\frac {{x}^{n-1}}{2\,a} \left ( -\tan \left ( {\frac {-\ln \left ( x \right ) +{\it \_C1}}{2}\sqrt {4\,ab-{n}^{2}+2\,n-1}} \right ) \sqrt {4\,ab-{n}^{2}+2\,n-1}+n-1 \right ) } \right \}$