2.373   ODE No. 373

\[ a^2 y(x)^2 \left (\log ^2(y(x))-1\right )+y'(x)^2=0 \]

✓ Mathematica : cpu = 0.243403 (sec), leaf count = 169

DSolve[a^2*(-1 + Log[y[x]]^2)*y[x]^2 + Derivative[1][y][x]^2 == 0,y[x],x]
 

\[\left \{\left \{y(x)\to \exp \left (-\frac {i \tan (a x-i c_1)}{\sqrt {-1-\tan ^2(a x-i c_1)}}\right )\right \},\left \{y(x)\to \exp \left (\frac {i \tan (a x-i c_1)}{\sqrt {-1-\tan ^2(a x-i c_1)}}\right )\right \},\left \{y(x)\to \exp \left (-\frac {i \tan (a x+i c_1)}{\sqrt {-1-\tan ^2(a x+i c_1)}}\right )\right \},\left \{y(x)\to \exp \left (\frac {i \tan (a x+i c_1)}{\sqrt {-1-\tan ^2(a x+i c_1)}}\right )\right \}\right \}\]

✓ Maple : cpu = 0.25 (sec), leaf count = 49

dsolve(diff(y(x),x)^2+a^2*y(x)^2*(ln(y(x))^2-1) = 0,y(x))
 

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