2.369   ODE No. 369

\[ -a^2+y'(x)^2+y(x)^2=0 \]

✓ Mathematica : cpu = 0.11645 (sec), leaf count = 107

DSolve[-a^2 + y[x]^2 + Derivative[1][y][x]^2 == 0,y[x],x]
 

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

✓ Maple : cpu = 0.132 (sec), leaf count = 68

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

\[y \left (x \right ) = a\]