#### 2.197   ODE No. 197

$\cos (x) y'(x)-y(x)^4-y(x) \sin (x)=0$ Mathematica : cpu = 0.106088 (sec), leaf count = 98

$\left \{\left \{y(x)\to \frac {1}{\sqrt [3]{-\sin (x)-2 \sin (x) \cos ^2(x)+c_1 \cos ^3(x)}}\right \},\left \{y(x)\to -\frac {\sqrt [3]{-1}}{\sqrt [3]{-\sin (x)-2 \sin (x) \cos ^2(x)+c_1 \cos ^3(x)}}\right \},\left \{y(x)\to \frac {(-1)^{2/3}}{\sqrt [3]{-\sin (x)-2 \sin (x) \cos ^2(x)+c_1 \cos ^3(x)}}\right \}\right \}$ Maple : cpu = 0.09 (sec), leaf count = 237

$\left \{ y \left ( x \right ) ={\frac {1}{{\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{4}+2\,\cos \left ( x \right ) \left ( \sin \left ( x \right ) \right ) ^{3}-2\,{\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{2}-3\,\cos \left ( x \right ) \sin \left ( x \right ) +{\it \_C1}}\sqrt [3]{\cos \left ( x \right ) \left ( {\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{4}+2\,\cos \left ( x \right ) \left ( \sin \left ( x \right ) \right ) ^{3}-2\,{\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{2}-3\,\cos \left ( x \right ) \sin \left ( x \right ) +{\it \_C1} \right ) ^{2}}},y \left ( x \right ) ={\frac {i\sqrt {3}-1}{2\,{\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{4}+4\,\cos \left ( x \right ) \left ( \sin \left ( x \right ) \right ) ^{3}-4\,{\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{2}-6\,\cos \left ( x \right ) \sin \left ( x \right ) +2\,{\it \_C1}}\sqrt [3]{\cos \left ( x \right ) \left ( {\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{4}+2\,\cos \left ( x \right ) \left ( \sin \left ( x \right ) \right ) ^{3}-2\,{\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{2}-3\,\cos \left ( x \right ) \sin \left ( x \right ) +{\it \_C1} \right ) ^{2}}},y \left ( x \right ) =-{\frac {1+i\sqrt {3}}{2\,{\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{4}+4\,\cos \left ( x \right ) \left ( \sin \left ( x \right ) \right ) ^{3}-4\,{\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{2}-6\,\cos \left ( x \right ) \sin \left ( x \right ) +2\,{\it \_C1}}\sqrt [3]{\cos \left ( x \right ) \left ( {\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{4}+2\,\cos \left ( x \right ) \left ( \sin \left ( x \right ) \right ) ^{3}-2\,{\it \_C1}\, \left ( \sin \left ( x \right ) \right ) ^{2}-3\,\cos \left ( x \right ) \sin \left ( x \right ) +{\it \_C1} \right ) ^{2}}} \right \}$