2.208   ODE No. 208

\[ a y(x)^2-b \cos (c+x)+y(x) y'(x)=0 \] Mathematica : cpu = 0.21905 (sec), leaf count = 118


\[\left \{\left \{y(x)\to -\frac {\sqrt {4 a^2 c_1 e^{-2 a x}+4 a b \cos (c+x)+c_1 e^{-2 a x}+2 b \sin (c+x)}}{\sqrt {4 a^2+1}}\right \},\left \{y(x)\to \frac {\sqrt {4 a^2 c_1 e^{-2 a x}+4 a b \cos (c+x)+c_1 e^{-2 a x}+2 b \sin (c+x)}}{\sqrt {4 a^2+1}}\right \}\right \}\] Maple : cpu = 0.083 (sec), leaf count = 106


\[y \relax (x ) = \frac {\sqrt {16 c_{1} \left (a^{2}+\frac {1}{4}\right )^{2} {\mathrm e}^{-2 a x}+16 \left (a \cos \left (x +c \right )+\frac {\sin \left (x +c \right )}{2}\right ) \left (a^{2}+\frac {1}{4}\right ) b}}{4 a^{2}+1}\]