\[ y'(x)=\frac {x^2 y(x) \sqrt {x^2+y(x)^2}+x^3 \left (-\sqrt {x^2+y(x)^2}\right )+y(x)}{x} \] ✓ Mathematica : cpu = 0.278409 (sec), leaf count = 221
DSolve[Derivative[1][y][x] == (y[x] - x^3*Sqrt[x^2 + y[x]^2] + x^2*y[x]*Sqrt[x^2 + y[x]^2])/x,y[x],x]
\[\left \{\left \{y(x)\to \frac {x-2 \sqrt {x^2 \tanh ^2\left (\frac {1}{3} \left (-\sqrt {2} x^3-3 \sqrt {2} c_1\right )\right )-x^2 \tanh ^4\left (\frac {1}{3} \left (-\sqrt {2} x^3-3 \sqrt {2} c_1\right )\right )}}{-1+2 \tanh ^2\left (\frac {1}{3} \left (-\sqrt {2} x^3-3 \sqrt {2} c_1\right )\right )}\right \},\left \{y(x)\to \frac {x+2 \sqrt {x^2 \tanh ^2\left (\frac {1}{3} \left (-\sqrt {2} x^3-3 \sqrt {2} c_1\right )\right )-x^2 \tanh ^4\left (\frac {1}{3} \left (-\sqrt {2} x^3-3 \sqrt {2} c_1\right )\right )}}{-1+2 \tanh ^2\left (\frac {1}{3} \left (-\sqrt {2} x^3-3 \sqrt {2} c_1\right )\right )}\right \}\right \}\] ✓ Maple : cpu = 0.192 (sec), leaf count = 49
dsolve(diff(y(x),x) = -(-y(x)+x^3*(y(x)^2+x^2)^(1/2)-x^2*(y(x)^2+x^2)^(1/2)*y(x))/x,y(x))
\[\ln \left (\frac {2 x \left (\sqrt {2 y \left (x \right )^{2}+2 x^{2}}+y \left (x \right )+x \right )}{y \left (x \right )-x}\right )+\frac {\sqrt {2}\, x^{3}}{3}-\ln \left (x \right )-c_{1} = 0\]