2.197   ODE No. 197

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

\[ \cos (x) y'(x)-y(x)^4-y(x) \sin (x)=0 \] Mathematica : cpu = 0.134098 (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 = 0.158 (sec), leaf count = 237

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