#### 2.45   ODE No. 45

$2 y(x)^3 \left (a^2 x^3-b^2 x\right )+3 b y(x)^2+y'(x)=0$ Mathematica : cpu = 0.499621 (sec), leaf count = 133

$\text {Solve}\left [c_1=\sqrt [4]{\left (\frac {b}{a x}-\frac {1}{a x^2 y(x)}\right )^2-1} \left (-\frac {\left (\frac {b}{a x}-\frac {1}{a x^2 y(x)}\right ) \, _2F_1\left (\frac {1}{2},\frac {3}{4};\frac {3}{2};\left (\frac {b}{a x}-\frac {1}{a x^2 y(x)}\right )^2\right )}{2 \sqrt [4]{1-\left (\frac {b}{a x}-\frac {1}{a x^2 y(x)}\right )^2}}-\frac {a x}{b}\right ),y(x)\right ]$ Maple : cpu = 0.096 (sec), leaf count = 123

$\left \{ {\it \_C1}+{1\sqrt [4]{ \left ( {\frac {ax}{b}}+ \left ( {\frac {{b}^{2}y \left ( x \right ) }{a}}-{\frac {b}{ax}} \right ) ^{-1} \right ) ^{2}-1} \left ( {\frac {{b}^{2}y \left ( x \right ) }{a}}-{\frac {b}{ax}} \right ) ^{-1}{\frac {1}{\sqrt {{\frac {ax}{b}}+ \left ( {\frac {{b}^{2}y \left ( x \right ) }{a}}-{\frac {b}{ax}} \right ) ^{-1}}}}}-\int ^{{\frac {a{x}^{2}y \left ( x \right ) }{bxy \left ( x \right ) -1}}}\!{1\sqrt [4]{{{\it \_a}}^{2}-1}{\frac {1}{\sqrt {{\it \_a}}}}}{d{\it \_a}}=0 \right \}$