3.45   ODE No. 45

\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +2\, \left ( {a}^{2}{x}^{3}-{b}^{2}x \right ) \left ( y \left ( x \right ) \right ) ^{3}+3\,b \left ( y \left ( x \right ) \right ) ^{2}=0} \]

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

Mathematica: cpu = 0.522566 (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 = 0.094 (sec), leaf count = 123 \[ \left \{ {\it \_C1}+{1\sqrt [4]{ \left ( {\frac {ax}{b}}+ \left ( { \frac {{b}^{2}y \left ( x \right ) }{a}}-{\frac {b}{ax}} \right ) ^{-1} \right ) ^{2}-1} \left ( {\frac {{b}^{2}y \left ( x \right ) }{a}}-{ \frac {b}{ax}} \right ) ^{-1}{\frac {1}{\sqrt {{\frac {ax}{b}}+ \left ( {\frac {{b}^{2}y \left ( x \right ) }{a}}-{\frac {b}{ax}} \right ) ^{-1}} }}}-\int ^{{\frac {a{x}^{2}y \left ( x \right ) }{bxy \left ( x \right ) - 1}}}\!{1\sqrt [4]{{{\it \_a}}^{2}-1}{\frac {1}{\sqrt {{\it \_a}}}}}{d{ \it \_a}}=0 \right \} \]

Sage: cpu = 0 (sec), leaf count = 0 \[ \text {Maxima was unable to solve this ODE} \]