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 = 0.0430559 (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 = 0.056 (sec), leaf count = 32

\[\{y \left (x \right ) = c_{1} {\mathrm e}^{x}, y \left (x \right ) = c_{1}-\cos \left (x \right ), y \left (x \right ) = c_{1}-\ln \left (-\cot \left (x \right )+\csc \left (x \right )\right )\}\]