\[ y'(x)=-\frac {i x \left (x^8+8 x^4 y(x)^2+16 i x^2+16 y(x)^4\right )}{32 y(x)} \] ✓ Mathematica : cpu = 0.0916419 (sec), leaf count = 360
DSolve[Derivative[1][y][x] == ((-1/32*I)*x*((16*I)*x^2 + x^8 + 8*x^4*y[x]^2 + 16*y[x]^4))/y[x],y[x],x]
\[\left \{\left \{y(x)\to -\frac {\sqrt {\left (Y_{\frac {1}{3}}\left (\left (\frac {1}{3}-\frac {i}{3}\right ) x^3\right )+c_1 J_{\frac {1}{3}}\left (\left (\frac {1}{3}-\frac {i}{3}\right ) x^3\right )\right ) \left ((1+i) x^3 \left (Y_{\frac {4}{3}}\left (\left (\frac {1}{3}-\frac {i}{3}\right ) x^3\right )+c_1 J_{\frac {4}{3}}\left (\left (\frac {1}{3}-\frac {i}{3}\right ) x^3\right )\right )-\frac {1}{4} \left (x^6+8 i\right ) Y_{\frac {1}{3}}\left (\left (\frac {1}{3}-\frac {i}{3}\right ) x^3\right )-\frac {1}{4} c_1 \left (x^6+8 i\right ) J_{\frac {1}{3}}\left (\left (\frac {1}{3}-\frac {i}{3}\right ) x^3\right )\right )}}{x \left (Y_{\frac {1}{3}}\left (\left (\frac {1}{3}-\frac {i}{3}\right ) x^3\right )+c_1 J_{\frac {1}{3}}\left (\left (\frac {1}{3}-\frac {i}{3}\right ) x^3\right )\right )}\right \},\left \{y(x)\to \frac {\sqrt {\left (Y_{\frac {1}{3}}\left (\left (\frac {1}{3}-\frac {i}{3}\right ) x^3\right )+c_1 J_{\frac {1}{3}}\left (\left (\frac {1}{3}-\frac {i}{3}\right ) x^3\right )\right ) \left ((1+i) x^3 \left (Y_{\frac {4}{3}}\left (\left (\frac {1}{3}-\frac {i}{3}\right ) x^3\right )+c_1 J_{\frac {4}{3}}\left (\left (\frac {1}{3}-\frac {i}{3}\right ) x^3\right )\right )-\frac {1}{4} \left (x^6+8 i\right ) Y_{\frac {1}{3}}\left (\left (\frac {1}{3}-\frac {i}{3}\right ) x^3\right )-\frac {1}{4} c_1 \left (x^6+8 i\right ) J_{\frac {1}{3}}\left (\left (\frac {1}{3}-\frac {i}{3}\right ) x^3\right )\right )}}{x \left (Y_{\frac {1}{3}}\left (\left (\frac {1}{3}-\frac {i}{3}\right ) x^3\right )+c_1 J_{\frac {1}{3}}\left (\left (\frac {1}{3}-\frac {i}{3}\right ) x^3\right )\right )}\right \}\right \}\] ✓ Maple : cpu = 0.617 (sec), leaf count = 251
dsolve(diff(y(x),x) = -1/32*I*(16*I*x^2+16*y(x)^4+8*x^4*y(x)^2+x^8)*x/y(x),y(x))
\[y \left (x \right ) = -\frac {\sqrt {4}\, \sqrt {\left (\BesselJ \left (\frac {1}{3}, \left (\frac {1}{3}-\frac {i}{3}\right ) x^{3}\right ) c_{1}+\BesselY \left (\frac {1}{3}, \left (\frac {1}{3}-\frac {i}{3}\right ) x^{3}\right )\right ) \left (-2 \left (\frac {x^{6}}{8}+i\right ) c_{1} \BesselJ \left (\frac {1}{3}, \left (\frac {1}{3}-\frac {i}{3}\right ) x^{3}\right )+\left (-\frac {x^{6}}{4}-2 i\right ) \BesselY \left (\frac {1}{3}, \left (\frac {1}{3}-\frac {i}{3}\right ) x^{3}\right )+\left (1+i\right ) \left (c_{1} \BesselJ \left (\frac {4}{3}, \left (\frac {1}{3}-\frac {i}{3}\right ) x^{3}\right )+\BesselY \left (\frac {4}{3}, \left (\frac {1}{3}-\frac {i}{3}\right ) x^{3}\right )\right ) x^{3}\right )}}{2 \left (\BesselJ \left (\frac {1}{3}, \left (\frac {1}{3}-\frac {i}{3}\right ) x^{3}\right ) c_{1}+\BesselY \left (\frac {1}{3}, \left (\frac {1}{3}-\frac {i}{3}\right ) x^{3}\right )\right ) x}\]