2.539   ODE No. 539

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

\[ \sin (x) y'(x)^3-y'(x)^2 \left (y(x) \sin (x)-\cos ^2(x)\right )-y'(x) \left (y(x) \cos ^2(x)+\sin (x)\right )+y(x) \sin (x)=0 \] Mathematica : cpu = 0.0271125 (sec), leaf count = 45

\[\left \{\left \{y(x)\to c_1 e^x\right \},\{y(x)\to -\cos (x)+c_1\},\left \{y(x)\to -\log \left (\sin \left (\frac {x}{2}\right )\right )+\log \left (\cos \left (\frac {x}{2}\right )\right )+c_1\right \}\right \}\] Maple : cpu = 0.059 (sec), leaf count = 32

\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{x}},y \left ( x \right ) =-\cos \left ( x \right ) +{\it \_C1},y \left ( x \right ) =-\ln \left ( \csc \left ( x \right ) -\cot \left ( x \right ) \right ) +{\it \_C1} \right \} \]