3.197   ODE No. 197

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

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

Mathematica: cpu = 0.041005 (sec), leaf count = 98 $$\{\{y(x)\to \frac{1}{\sqrt[3]{c_1{\cos }^3(x)-\sin (x)-2\sin (x){\cos }^2(x)}}\},\{y(x)\to -\frac{\sqrt[3]{-1}}{\sqrt[3]{c_1{\cos }^3(x)-\sin (x)-2\sin (x){\cos }^2(x)}}\},\{y(x)\to \frac{(-1{)}^{2/3}}{\sqrt[3]{c_1{\cos }^3(x)-\sin (x)-2\sin (x){\cos }^2(x)}}\}\}$$

Maple: cpu = 0.031 (sec), leaf count = 364 $$\{y\left(x\right)=\frac{1}{\mathit{\_}\mathit{C}\mathit{1}{(\sin \left(x\right))}^4+2\cos \left(x\right){(\sin \left(x\right))}^3-2\mathit{\_}\mathit{C}\mathit{1}{(\sin \left(x\right))}^2-3\cos \left(x\right)\sin \left(x\right)+\mathit{\_}\mathit{C}\mathit{1}}\sqrt[3]{\cos \left(x\right){(\mathit{\_}\mathit{C}\mathit{1}{(\sin \left(x\right))}^4+2\cos \left(x\right){(\sin \left(x\right))}^3-2\mathit{\_}\mathit{C}\mathit{1}{(\sin \left(x\right))}^2-3\cos \left(x\right)\sin \left(x\right)+\mathit{\_}\mathit{C}\mathit{1})}^2},y\left(x\right)=-\frac{1}{2\mathit{\_}\mathit{C}\mathit{1}{(\sin \left(x\right))}^4+4\cos \left(x\right){(\sin \left(x\right))}^3-4\mathit{\_}\mathit{C}\mathit{1}{(\sin \left(x\right))}^2-6\cos \left(x\right)\sin \left(x\right)+2\mathit{\_}\mathit{C}\mathit{1}}\sqrt[3]{\cos \left(x\right){(\mathit{\_}\mathit{C}\mathit{1}{(\sin \left(x\right))}^4+2\cos \left(x\right){(\sin \left(x\right))}^3-2\mathit{\_}\mathit{C}\mathit{1}{(\sin \left(x\right))}^2-3\cos \left(x\right)\sin \left(x\right)+\mathit{\_}\mathit{C}\mathit{1})}^2}-\frac{\frac{i}{2}\sqrt{3}}{\mathit{\_}\mathit{C}\mathit{1}{(\sin \left(x\right))}^4+2\cos \left(x\right){(\sin \left(x\right))}^3-2\mathit{\_}\mathit{C}\mathit{1}{(\sin \left(x\right))}^2-3\cos \left(x\right)\sin \left(x\right)+\mathit{\_}\mathit{C}\mathit{1}}\sqrt[3]{\cos \left(x\right){(\mathit{\_}\mathit{C}\mathit{1}{(\sin \left(x\right))}^4+2\cos \left(x\right){(\sin \left(x\right))}^3-2\mathit{\_}\mathit{C}\mathit{1}{(\sin \left(x\right))}^2-3\cos \left(x\right)\sin \left(x\right)+\mathit{\_}\mathit{C}\mathit{1})}^2},y\left(x\right)=-\frac{1}{2\mathit{\_}\mathit{C}\mathit{1}{(\sin \left(x\right))}^4+4\cos \left(x\right){(\sin \left(x\right))}^3-4\mathit{\_}\mathit{C}\mathit{1}{(\sin \left(x\right))}^2-6\cos \left(x\right)\sin \left(x\right)+2\mathit{\_}\mathit{C}\mathit{1}}\sqrt[3]{\cos \left(x\right){(\mathit{\_}\mathit{C}\mathit{1}{(\sin \left(x\right))}^4+2\cos \left(x\right){(\sin \left(x\right))}^3-2\mathit{\_}\mathit{C}\mathit{1}{(\sin \left(x\right))}^2-3\cos \left(x\right)\sin \left(x\right)+\mathit{\_}\mathit{C}\mathit{1})}^2}+\frac{\frac{i}{2}\sqrt{3}}{\mathit{\_}\mathit{C}\mathit{1}{(\sin \left(x\right))}^4+2\cos \left(x\right){(\sin \left(x\right))}^3-2\mathit{\_}\mathit{C}\mathit{1}{(\sin \left(x\right))}^2-3\cos \left(x\right)\sin \left(x\right)+\mathit{\_}\mathit{C}\mathit{1}}\sqrt[3]{\cos \left(x\right){(\mathit{\_}\mathit{C}\mathit{1}{(\sin \left(x\right))}^4+2\cos \left(x\right){(\sin \left(x\right))}^3-2\mathit{\_}\mathit{C}\mathit{1}{(\sin \left(x\right))}^2-3\cos \left(x\right)\sin \left(x\right)+\mathit{\_}\mathit{C}\mathit{1})}^2}\}$$