\[ y'(x)=-\frac {i \left (x^4+8 x^2 y(x)^2+16 y(x)^4+8 i x\right )}{32 y(x)} \] ✓ Mathematica : cpu = 0.096443 (sec), leaf count = 406
DSolve[Derivative[1][y][x] == ((-1/32*I)*((8*I)*x + x^4 + 8*x^2*y[x]^2 + 16*y[x]^4))/y[x],y[x],x]
\[\left \{\left \{y(x)\to -\frac {\sqrt {2} \sqrt {\left (\text {Bi}\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )+c_1 \text {Ai}\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )\right ) \left (-\frac {1}{2} x^2 \left (\text {Bi}\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )+c_1 \text {Ai}\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )\right )+\left (1+i \sqrt {3}\right ) \text {Bi}'\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )+\left (1+i \sqrt {3}\right ) c_1 \text {Ai}'\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )\right )}}{2 \text {Bi}\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )+2 c_1 \text {Ai}\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )}\right \},\left \{y(x)\to \frac {\sqrt {2} \sqrt {\left (\text {Bi}\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )+c_1 \text {Ai}\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )\right ) \left (-\frac {1}{2} x^2 \left (\text {Bi}\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )+c_1 \text {Ai}\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )\right )+\left (1+i \sqrt {3}\right ) \text {Bi}'\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )+\left (1+i \sqrt {3}\right ) c_1 \text {Ai}'\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )\right )}}{2 \text {Bi}\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )+2 c_1 \text {Ai}\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )}\right \}\right \}\] ✓ Maple : cpu = 0.597 (sec), leaf count = 296
dsolve(diff(y(x),x) = -1/32*I*(8*I*x+16*y(x)^4+8*x^2*y(x)^2+x^4)/y(x),y(x))
\[y \left (x \right ) = -\frac {\sqrt {2}\, \sqrt {\left (\AiryAi \left (\frac {\left (i-\sqrt {3}\right ) x}{2}\right ) c_{1}+\AiryBi \left (\frac {\left (i-\sqrt {3}\right ) x}{2}\right )\right ) \left (\left (1+i \sqrt {3}\right ) c_{1} \AiryAi \left (1, \frac {\left (i-\sqrt {3}\right ) x}{2}\right )+\left (1+i \sqrt {3}\right ) \AiryBi \left (1, \frac {\left (i-\sqrt {3}\right ) x}{2}\right )-\frac {x^{2} \left (\AiryAi \left (\frac {\left (i-\sqrt {3}\right ) x}{2}\right ) c_{1}+\AiryBi \left (\frac {\left (i-\sqrt {3}\right ) x}{2}\right )\right )}{2}\right )}}{2 \AiryAi \left (\frac {\left (i-\sqrt {3}\right ) x}{2}\right ) c_{1}+2 \AiryBi \left (\frac {\left (i-\sqrt {3}\right ) x}{2}\right )}\]