2.197   ODE No. 197

\[ \cos (x) y'(x)-y(x)^4-y(x) \sin (x)=0 \]

✓ Mathematica : cpu = 0.0762773 (sec), leaf count = 104

DSolve[-(Sin[x]*y[x]) - y[x]^4 + Cos[x]*Derivative[1][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to \frac {1}{\sqrt [3]{-\sin ^3(x)+c_1 \cos ^3(x)-3 \sin (x) \cos ^2(x)}}\right \},\left \{y(x)\to -\frac {\sqrt [3]{-1}}{\sqrt [3]{-\sin ^3(x)+c_1 \cos ^3(x)-3 \sin (x) \cos ^2(x)}}\right \},\left \{y(x)\to \frac {(-1)^{2/3}}{\sqrt [3]{-\sin ^3(x)+c_1 \cos ^3(x)-3 \sin (x) \cos ^2(x)}}\right \}\right \}\]

✓ Maple : cpu = 0.251 (sec), leaf count = 237

dsolve(cos(x)*diff(y(x),x)-y(x)^4-y(x)*sin(x) = 0,y(x))
 

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