2.488   ODE No. 488

\[ 4 a^2-4 a y(x) y'(x)-4 a x+y(x)^2 y'(x)^2+y(x)^2=0 \] Mathematica : cpu = 0.305845 (sec), leaf count = 85


\[\left \{\left \{y(x)\to -\frac {\sqrt {16 a^3 x-4 a^2 x^2-4 a c_1 x-c_1{}^2}}{2 a}\right \},\left \{y(x)\to \frac {\sqrt {16 a^3 x-4 a^2 x^2-4 a c_1 x-c_1{}^2}}{2 a}\right \}\right \}\] Maple : cpu = 0.607 (sec), leaf count = 111


\[y \relax (x ) = -2 \sqrt {a x}\]