3.21   ODE No. 21

\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( y \left ( x \right ) \right ) ^{2}+y \left ( x \right ) \sin \left ( x \right ) -\cos \left ( x \right ) =0} \]

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

Mathematica: cpu = 7.447446 (sec), leaf count = 69 \[ \left \{\left \{y(x)\to -\frac {c_1 \left (1-\sin (x) e^{\cos (x)} \left (\int _1^x e^{-\cos (K[1])} \, dK[1]\right )\right )-\sin (x) e^{\cos (x)}}{c_1 e^{\cos (x)} \int _1^x e^{-\cos (K[1])} \, dK[1]+e^{\cos (x)}}\right \}\right \} \]

Maple: cpu = 0.093 (sec), leaf count = 25 \[ \left \{ y \left ( x \right ) =-{\frac {{{\rm e}^{-\cos \left ( x \right ) }}}{{\it \_C1}+\int \!{{\rm e}^{-\cos \left ( x \right ) }} \,{\rm d}x}}+\sin \left ( x \right ) \right \} \]

Sage: cpu = 3.404 (sec), leaf count = 0 \[ \left [\left [y\left (x\right ) = \frac {c e^{\cos \left (x\right )} \sin \left (x\right ) + e^{\cos \left (x\right )} \int e^{\left (-\cos \left (x\right )\right )}\,{d x} \sin \left (x\right ) - 1}{c e^{\cos \left (x\right )} + e^{\cos \left (x\right )} \int e^{\left (-\cos \left (x\right )\right )}\,{d x}}\right ], \text {\texttt {riccati}}\right ] \]