2.342   ODE No. 342

\[ x \left (2 e^{-x y(x)}+3 e^{x y(x)}\right ) \left (x y'(x)+y(x)\right )+1=0 \] Mathematica : cpu = 0.544607 (sec), leaf count = 163


\[\left \{\left \{y(x)\to -\frac {\cosh ^{-1}\left (\frac {1}{24} \left (-5 \sqrt {24+\log ^2\left (\frac {c_1}{x}\right )}-\log \left (\frac {c_1}{x}\right )\right )\right )}{x}\right \},\left \{y(x)\to \frac {\cosh ^{-1}\left (\frac {1}{24} \left (-5 \sqrt {24+\log ^2\left (\frac {c_1}{x}\right )}-\log \left (\frac {c_1}{x}\right )\right )\right )}{x}\right \},\left \{y(x)\to -\frac {\cosh ^{-1}\left (\frac {1}{24} \left (5 \sqrt {24+\log ^2\left (\frac {c_1}{x}\right )}-\log \left (\frac {c_1}{x}\right )\right )\right )}{x}\right \},\left \{y(x)\to \frac {\cosh ^{-1}\left (\frac {1}{24} \left (5 \sqrt {24+\log ^2\left (\frac {c_1}{x}\right )}-\log \left (\frac {c_1}{x}\right )\right )\right )}{x}\right \}\right \}\] Maple : cpu = 0.048 (sec), leaf count = 17


\[y \relax (x ) = \frac {\ln \left (-\frac {\ln \relax (x )}{5}+\frac {c_{1}}{5}\right )}{x}\]