ODE No. 494

\[ \left (y(x)^2-a^2 x^2\right ) y'(x)^2+\left (1-a^2\right ) x^2+2 x y(x) y'(x)=0 \]

✓ Mathematica : cpu = 0.0821509 (sec), leaf count = 49

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

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

✓ Maple : cpu = 0.203 (sec), leaf count = 159

dsolve((y(x)^2-a^2*x^2)*diff(y(x),x)^2+2*x*y(x)*diff(y(x),x)+(-a^2+1)*x^2 = 0,y(x))

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