2.359   ODE No. 359

\[ 3 \sin (x) y'(x) \sin (y(x))+5 y(x) \cos ^4(x)=0 \] Mathematica : cpu = 0.317546 (sec), leaf count = 45


\[\left \{\left \{y(x)\to \text {SinIntegral}^{(-1)}\left (-\frac {5}{3} \left (\frac {5 \cos (x)}{4}+\frac {1}{12} \cos (3 x)+\log \left (\sin \left (\frac {x}{2}\right )\right )-\log \left (\cos \left (\frac {x}{2}\right )\right )\right )+c_1\right )\right \}\right \}\] Maple : cpu = 0.072 (sec), leaf count = 28


\[\frac {3 \Si \left (y \relax (x )\right )}{5}+c_{1}+\ln \left (\csc \relax (x )-\cot \relax (x )\right )+\frac {\cos \left (3 x \right )}{12}+\frac {5 \cos \relax (x )}{4} = 0\]