2.373   ODE No. 373

\[ a^2 y(x)^2 \left (\log ^2(y(x))-1\right )+y'(x)^2=0 \] Mathematica : cpu = 0.291367 (sec), leaf count = 185


\[\left \{\left \{y(x)\to \exp \left (-\frac {1}{2} \sqrt {-e^{2 i a x-2 c_1}-e^{2 c_1-2 i a x}+2}\right )\right \},\left \{y(x)\to \exp \left (\frac {1}{2} \sqrt {-e^{2 i a x-2 c_1}-e^{2 c_1-2 i a x}+2}\right )\right \},\left \{y(x)\to \exp \left (-\frac {1}{2} \sqrt {-e^{-2 i a x-2 c_1}-e^{2 i a x+2 c_1}+2}\right )\right \},\left \{y(x)\to \exp \left (\frac {1}{2} \sqrt {-e^{-2 i a x-2 c_1}-e^{2 i a x+2 c_1}+2}\right )\right \}\right \}\] Maple : cpu = 0.226 (sec), leaf count = 49


\[y \relax (x ) = {\mathrm e}^{\RootOf \left (a^{2} {\mathrm e}^{2 \textit {\_Z}} \left (\textit {\_Z}^{2}-1\right )\right )}\]