3.32   ODE No. 32

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

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

Mathematica: cpu = 0.237030 (sec), leaf count = 34 \[ \left \{\left \{y(x)\to \frac {\csc (x) \left (c_1 \tan (x) \sec (x)-2 \sin (x) \cos (x)\right )}{c_1 \sec (x)+\cos ^2(x)}\right \}\right \} \]

Maple: cpu = 0.218 (sec), leaf count = 28 \[ \left \{ y \left ( x \right ) =-2\,{\frac { \left ( \cos \left ( x \right ) \right ) ^{3}{\it \_C1}+1}{ \left ( \left ( \cos \left ( x \right ) \right ) ^{3}{\it \_C1}-2 \right ) \cos \left ( x \right ) }} \right \} \]

Sage: cpu = 0.064 (sec), leaf count = 0 \[ \left [\left [y\left (x\right ) = -\frac {{\left (c - 3 i\right )} \cosh \left (\frac {3}{2} \, \log \left (\cos \left (x\right )\right )\right ) + {\left (3 \, c - i\right )} \sinh \left (\frac {3}{2} \, \log \left (\cos \left (x\right )\right )\right )}{2 \, c \cos \left (x\right ) \cosh \left (\frac {3}{2} \, \log \left (\cos \left (x\right )\right )\right ) - 2 i \, \cos \left (x\right ) \sinh \left (\frac {3}{2} \, \log \left (\cos \left (x\right )\right )\right )}\right ], \text {\texttt {riccati}}\right ] \]