2.197   ODE No. 197

\[ \cos (x) y'(x)-y(x)^4-y(x) \sin (x)=0 \] Mathematica : cpu = 0.121139 (sec), leaf count = 98


\[\left \{\left \{y(x)\to \frac {1}{\sqrt [3]{-\sin (x)+c_1 \cos ^3(x)-2 \sin (x) \cos ^2(x)}}\right \},\left \{y(x)\to -\frac {\sqrt [3]{-1}}{\sqrt [3]{-\sin (x)+c_1 \cos ^3(x)-2 \sin (x) \cos ^2(x)}}\right \},\left \{y(x)\to \frac {(-1)^{2/3}}{\sqrt [3]{-\sin (x)+c_1 \cos ^3(x)-2 \sin (x) \cos ^2(x)}}\right \}\right \}\] Maple : cpu = 0.123 (sec), leaf count = 237


\[y \relax (x ) = \frac {\left (\cos \relax (x ) \left (c_{1} \left (\sin ^{4}\relax (x )\right )+2 \cos \relax (x ) \left (\sin ^{3}\relax (x )\right )-2 c_{1} \left (\sin ^{2}\relax (x )\right )-3 \sin \relax (x ) \cos \relax (x )+c_{1}\right )^{2}\right )^{\frac {1}{3}}}{c_{1} \left (\sin ^{4}\relax (x )\right )+2 \cos \relax (x ) \left (\sin ^{3}\relax (x )\right )-2 c_{1} \left (\sin ^{2}\relax (x )\right )-3 \sin \relax (x ) \cos \relax (x )+c_{1}}\]