3.539   ODE No. 539

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

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

Mathematica: cpu = 0.026503 (sec), leaf count = 45 \[ \left \{\left \{y(x)\to c_1 e^x\right \},\left \{y(x)\to c_1-\cos (x)\right \},\left \{y(x)\to c_1-\log \left (\sin \left (\frac {x}{2}\right )\right )+\log \left (\cos \left (\frac {x}{2}\right )\right )\right \}\right \} \]

Maple: cpu = 0.031 (sec), leaf count = 32 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{x}},y \left ( x \right ) =-\cos \left ( x \right ) +{\it \_C1},y \left ( x \right ) =-\ln \left ( \csc \left ( x \right ) -\cot \left ( x \right ) \right ) +{\it \_C1} \right \} \]