ODE No. 241

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

✓ Mathematica : cpu = 0.0998251 (sec), leaf count = 41

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

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

✓ Maple : cpu = 0.014 (sec), leaf count = 33

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

\[y \left (x \right ) = \sqrt {-a \,x^{2}+x c_{1}}\]