2.539   ODE No. 539

\[ \sin (x) y'(x)^3-y'(x)^2 \left (y(x) \sin (x)-\cos ^2(x)\right )-y'(x) \left (y(x) \cos ^2(x)+\sin (x)\right )+y(x) \sin (x)=0 \] Mathematica : cpu = 0.0329279 (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


\[y \relax (x ) = c_{1} {\mathrm e}^{x}\]