#### 2.98   ODE No. 98

$a y(x)^2+c x^{2 b}-b y(x)+x y'(x)=0$ Mathematica : cpu = 0.166358 (sec), leaf count = 442

$\left \{\left \{y(x)\to -\frac {\sqrt {-a} \sqrt {-c} x^b \left (-\frac {2 \sqrt {\frac {2}{\pi }} \cos \left (\frac {\sqrt {-a} \sqrt {-c} x^b}{b}\right )}{\sqrt {\frac {\sqrt {-a} \sqrt {-c} x^b}{b}}}+\frac {\sqrt {\frac {2}{\pi }} c_1 \sin \left (\frac {\sqrt {-a} \sqrt {-c} x^b}{b}\right )}{\sqrt {\frac {\sqrt {-a} \sqrt {-c} x^b}{b}}}-\frac {\sqrt {\frac {2}{\pi }} c_1 \left (-\sin \left (\frac {\sqrt {-a} \sqrt {-c} x^b}{b}\right )-\frac {\sqrt {-a} b \sqrt {-c} x^{-b} \cos \left (\frac {\sqrt {-a} \sqrt {-c} x^b}{b}\right )}{a c}\right )}{\sqrt {\frac {\sqrt {-a} \sqrt {-c} x^b}{b}}}\right )-\frac {\sqrt {\frac {2}{\pi }} b c_1 \cos \left (\frac {\sqrt {-a} \sqrt {-c} x^b}{b}\right )}{\sqrt {\frac {\sqrt {-a} \sqrt {-c} x^b}{b}}}}{2 a \left (\frac {\sqrt {\frac {2}{\pi }} \sin \left (\frac {\sqrt {-a} \sqrt {-c} x^b}{b}\right )}{\sqrt {\frac {\sqrt {-a} \sqrt {-c} x^b}{b}}}+\frac {\sqrt {\frac {2}{\pi }} c_1 \cos \left (\frac {\sqrt {-a} \sqrt {-c} x^b}{b}\right )}{\sqrt {\frac {\sqrt {-a} \sqrt {-c} x^b}{b}}}\right )}\right \}\right \}$ Maple : cpu = 0.053 (sec), leaf count = 38

$\left \{ y \left ( x \right ) =-{\frac {1}{{x}^{-b}}\tan \left ( {\frac {1}{b} \left ( \sqrt {a}{x}^{b}\sqrt {c}+{\it \_C1}\,b \right ) } \right ) \sqrt {c}{\frac {1}{\sqrt {a}}}} \right \}$