\[ -a^2+y(x)^2 y'(x)^2+y(x)^2=0 \] ✓ Mathematica : cpu = 0.0575558 (sec), leaf count = 117
DSolve[-a^2 + y[x]^2 + y[x]^2*Derivative[1][y][x]^2 == 0,y[x],x]
\[\left \{\left \{y(x)\to -\sqrt {a^2-x^2-2 c_1 x-c_1{}^2}\right \},\left \{y(x)\to \sqrt {a^2-x^2-2 c_1 x-c_1{}^2}\right \},\left \{y(x)\to -\sqrt {a^2-x^2+2 c_1 x-c_1{}^2}\right \},\left \{y(x)\to \sqrt {a^2-x^2+2 c_1 x-c_1{}^2}\right \}\right \}\] ✓ Maple : cpu = 0.297 (sec), leaf count = 54
dsolve(y(x)^2*diff(y(x),x)^2+y(x)^2-a^2 = 0,y(x))
\[y \left (x \right ) = a\]