\[ y'(x)=\frac {x^5 \left (-\sqrt {x^2+y(x)^2}\right )+x^4 y(x) \sqrt {x^2+y(x)^2}-x^4 \sqrt {x^2+y(x)^2}+x^3 y(x) \sqrt {x^2+y(x)^2}-x^2 \sqrt {x^2+y(x)^2}+x y(x) \sqrt {x^2+y(x)^2}+y(x)}{x} \] ✓ Mathematica : cpu = 0.346597 (sec), leaf count = 341
\[\left \{\left \{y(x)\to \frac {x-2 \sqrt {x^2 \tanh ^2\left (\frac {1}{20} \left (-4 \sqrt {2} x^5-5 \sqrt {2} x^4-10 \sqrt {2} x^2-20 \sqrt {2} c_1\right )\right )-x^2 \tanh ^4\left (\frac {1}{20} \left (-4 \sqrt {2} x^5-5 \sqrt {2} x^4-10 \sqrt {2} x^2-20 \sqrt {2} c_1\right )\right )}}{-1+2 \tanh ^2\left (\frac {1}{20} \left (-4 \sqrt {2} x^5-5 \sqrt {2} x^4-10 \sqrt {2} x^2-20 \sqrt {2} c_1\right )\right )}\right \},\left \{y(x)\to \frac {x+2 \sqrt {x^2 \tanh ^2\left (\frac {1}{20} \left (-4 \sqrt {2} x^5-5 \sqrt {2} x^4-10 \sqrt {2} x^2-20 \sqrt {2} c_1\right )\right )-x^2 \tanh ^4\left (\frac {1}{20} \left (-4 \sqrt {2} x^5-5 \sqrt {2} x^4-10 \sqrt {2} x^2-20 \sqrt {2} c_1\right )\right )}}{-1+2 \tanh ^2\left (\frac {1}{20} \left (-4 \sqrt {2} x^5-5 \sqrt {2} x^4-10 \sqrt {2} x^2-20 \sqrt {2} c_1\right )\right )}\right \}\right \}\] ✓ Maple : cpu = 0.527 (sec), leaf count = 62
\[ \left \{ \ln \left ( 2\,{\frac {x \left ( \sqrt {2\, \left ( y \left ( x \right ) \right ) ^{2}+2\,{x}^{2}}+y \left ( x \right ) +x \right ) }{y \left ( x \right ) -x}} \right ) +{\frac { \left ( 4\,{x}^{5}+5\,{x}^{4}+10\,{x}^{2} \right ) \sqrt {2}}{20}}-{\it \_C1}-\ln \left ( x \right ) =0 \right \} \]