\[ y'(x)=-\frac {i \left (x^4+8 x^2 y(x)^2+16 y(x)^4+8 i x\right )}{32 y(x)} \] ✓ Mathematica : cpu = 0.0740526 (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]
\[\left \{\left \{y(x)\to -\frac {\sqrt {2} \sqrt {\left (\operatorname {AiryBi}\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )+c_1 \operatorname {AiryAi}\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )\right ) \left (-\frac {1}{2} x^2 \left (\operatorname {AiryBi}\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )+c_1 \operatorname {AiryAi}\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )\right )+\left (1+i \sqrt {3}\right ) \operatorname {AiryBiPrime}\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )+\left (1+i \sqrt {3}\right ) c_1 \operatorname {AiryAiPrime}\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )\right )}}{2 \operatorname {AiryBi}\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )+2 c_1 \operatorname {AiryAi}\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )}\right \},\left \{y(x)\to \frac {\sqrt {2} \sqrt {\left (\operatorname {AiryBi}\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )+c_1 \operatorname {AiryAi}\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )\right ) \left (-\frac {1}{2} x^2 \left (\operatorname {AiryBi}\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )+c_1 \operatorname {AiryAi}\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )\right )+\left (1+i \sqrt {3}\right ) \operatorname {AiryBiPrime}\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )+\left (1+i \sqrt {3}\right ) c_1 \operatorname {AiryAiPrime}\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )\right )}}{2 \operatorname {AiryBi}\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )+2 c_1 \operatorname {AiryAi}\left (\frac {1}{2} \left (i-\sqrt {3}\right ) x\right )}\right \}\right \}\] ✓ Maple : cpu = 0.743 (sec), leaf count = 296
dsolve(diff(y(x),x) = -1/32*I*(8*I*x+16*y(x)^4+8*y(x)^2*x^2+x^4)/y(x),y(x))
\[y \left (x \right ) = -\frac {\sqrt {2}\, \sqrt {\left (c_{1} \left (1+i \sqrt {3}\right ) \operatorname {AiryAi}\left (1, \frac {\left (i-\sqrt {3}\right ) x}{2}\right )+\left (1+i \sqrt {3}\right ) \operatorname {AiryBi}\left (1, \frac {\left (i-\sqrt {3}\right ) x}{2}\right )-\frac {x^{2} \left (\operatorname {AiryAi}\left (\frac {\left (i-\sqrt {3}\right ) x}{2}\right ) c_{1}+\operatorname {AiryBi}\left (\frac {\left (i-\sqrt {3}\right ) x}{2}\right )\right )}{2}\right ) \left (\operatorname {AiryAi}\left (\frac {\left (i-\sqrt {3}\right ) x}{2}\right ) c_{1}+\operatorname {AiryBi}\left (\frac {\left (i-\sqrt {3}\right ) x}{2}\right )\right )}}{2 \operatorname {AiryAi}\left (\frac {\left (i-\sqrt {3}\right ) x}{2}\right ) c_{1}+2 \operatorname {AiryBi}\left (\frac {\left (i-\sqrt {3}\right ) x}{2}\right )}\]