2.369   ODE No. 369

\[ -a^2+y'(x)^2+y(x)^2=0 \] Mathematica : cpu = 0.0817852 (sec), leaf count = 107


\[\left \{\left \{y(x)\to -\frac {a \tan (x-c_1)}{\sqrt {1+\tan ^2(x-c_1)}}\right \},\left \{y(x)\to \frac {a \tan (x-c_1)}{\sqrt {1+\tan ^2(x-c_1)}}\right \},\left \{y(x)\to -\frac {a \tan (x+c_1)}{\sqrt {1+\tan ^2(x+c_1)}}\right \},\left \{y(x)\to \frac {a \tan (x+c_1)}{\sqrt {1+\tan ^2(x+c_1)}}\right \}\right \}\] Maple : cpu = 0.108 (sec), leaf count = 68


\[y \relax (x ) = a\]