3.359   ODE No. 359

$$\boxed{{\displaystyle 3\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)\sin \left(x\right)\sin \left(y\left(x\right)\right)+5{(\cos \left(x\right))}^{4}y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.055507 (sec), leaf count = 45 $$\left\{\{y(x)\to {\text{SinIntegral}}^{(-1)}(c_1-\frac{5}{3}(\frac{5\cos (x)}{4}+\frac{1}{12}\cos (3x)+\log (\sin \left(\frac{x}{2}\right))-\log (\cos \left(\frac{x}{2}\right))))\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 28 $$\{\frac{\cos \left(3x\right)}{12}+\frac{5\cos \left(x\right)}{4}+\ln (\csc \left(x\right)-\cot \left(x\right))+\frac{3\mathit{S}\mathit{i}\left(y\left(x\right)\right)}{5}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$