2.508   ODE No. 508

\[ \left (x^2 y(x)^2-x^2+y(x)^4\right ) y'(x)^2+2 x y(x) y'(x)-y(x)^2=0 \]

✓ Mathematica : cpu = 1.07967 (sec), leaf count = 62

DSolve[-y[x]^2 + 2*x*y[x]*Derivative[1][y][x] + (-x^2 + x^2*y[x]^2 + y[x]^4)*Derivative[1][y][x]^2 == 0,y[x],x]
 

\[\text {Solve}\left [\frac {\sqrt {x^2+y(x)^2} y(x) \tanh ^{-1}\left (\frac {x}{\sqrt {x^2+y(x)^2}}\right )}{x^2 \sqrt {\frac {y(x)^2 \left (x^2+y(x)^2\right )}{x^4}}}+y(x)=c_1,y(x)\right ]\]

✓ Maple : cpu = 0.627 (sec), leaf count = 60

dsolve((y(x)^4+y(x)^2*x^2-x^2)*diff(y(x),x)^2+2*x*y(x)*diff(y(x),x)-y(x)^2=0,y(x))
 

\[y \left (x \right ) = -i x\]