ODE No. 450

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

✓ Mathematica : cpu = 0.290986 (sec), leaf count = 26

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

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

✓ Maple : cpu = 0.737 (sec), leaf count = 51

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

\[y \left (x \right ) = \sqrt {a^{2}-x^{2}}\]