ODE No. 449

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

✓ Mathematica : cpu = 0.0360069 (sec), leaf count = 27

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

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

✓ Maple : cpu = 0.013 (sec), leaf count = 23

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

\[y \left (x \right ) = \frac {c_{1}}{a -x}\]