2.208   ODE No. 208

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

\[ a y(x)^2-b \cos (c+x)+y(x) y'(x)=0 \] Mathematica : cpu = 0.0704223 (sec), leaf count = 120

\[\left \{\left \{y(x)\to -\frac {\sqrt {e^{-2 a x} \left (4 a^2 c_1+2 b e^{2 a x} \sin (c+x)+c_1\right )+4 a b \cos (c+x)}}{\sqrt {4 a^2+1}}\right \},\left \{y(x)\to \frac {\sqrt {e^{-2 a x} \left (4 a^2 c_1+2 b e^{2 a x} \sin (c+x)+c_1\right )+4 a b \cos (c+x)}}{\sqrt {4 a^2+1}}\right \}\right \}\]

Maple : cpu = 0.073 (sec), leaf count = 106

\[ \left \{ y \left ( x \right ) ={\frac {1}{4\,{a}^{2}+1}\sqrt {16\, \left ( {a}^{2}+1/4 \right ) ^{2}{\it \_C1}\,{{\rm e}^{-2\,ax}}+16\, \left ( \cos \left ( x+c \right ) a+1/2\,\sin \left ( x+c \right ) \right ) \left ( {a}^{2}+1/4 \right ) b}},y \left ( x \right ) =-{\frac {1}{4\,{a}^{2}+1}\sqrt {16\, \left ( {a}^{2}+1/4 \right ) ^{2}{\it \_C1}\,{{\rm e}^{-2\,ax}}+16\, \left ( \cos \left ( x+c \right ) a+1/2\,\sin \left ( x+c \right ) \right ) \left ( {a}^{2}+1/4 \right ) b}} \right \} \]