\[ y'(x)=-\frac {i \left (x^4+2 x^2 y(x)^2+y(x)^4+i x\right )}{y(x)} \] ✓ Mathematica : cpu = 0.082101 (sec), leaf count = 274
DSolve[Derivative[1][y][x] == ((-I)*(I*x + x^4 + 2*x^2*y[x]^2 + y[x]^4))/y[x],y[x],x]
\[\left \{\left \{y(x)\to -\frac {\sqrt {2} \sqrt {\left (\text {Bi}\left (2 (-1)^{5/6} x\right )+c_1 \text {Ai}\left (2 (-1)^{5/6} x\right )\right ) \left (-2 x^2 \left (\text {Bi}\left (2 (-1)^{5/6} x\right )+c_1 \text {Ai}\left (2 (-1)^{5/6} x\right )\right )+\left (1+i \sqrt {3}\right ) \text {Bi}'\left (2 (-1)^{5/6} x\right )+\left (1+i \sqrt {3}\right ) c_1 \text {Ai}'\left (2 (-1)^{5/6} x\right )\right )}}{2 \text {Bi}\left (2 (-1)^{5/6} x\right )+2 c_1 \text {Ai}\left (2 (-1)^{5/6} x\right )}\right \},\left \{y(x)\to \frac {\sqrt {2} \sqrt {\left (\text {Bi}\left (2 (-1)^{5/6} x\right )+c_1 \text {Ai}\left (2 (-1)^{5/6} x\right )\right ) \left (-2 x^2 \left (\text {Bi}\left (2 (-1)^{5/6} x\right )+c_1 \text {Ai}\left (2 (-1)^{5/6} x\right )\right )+\left (1+i \sqrt {3}\right ) \text {Bi}'\left (2 (-1)^{5/6} x\right )+\left (1+i \sqrt {3}\right ) c_1 \text {Ai}'\left (2 (-1)^{5/6} x\right )\right )}}{2 \text {Bi}\left (2 (-1)^{5/6} x\right )+2 c_1 \text {Ai}\left (2 (-1)^{5/6} x\right )}\right \}\right \}\] ✓ Maple : cpu = 0.551 (sec), leaf count = 232
dsolve(diff(y(x),x) = -I*(I*x+x^4+2*x^2*y(x)^2+y(x)^4)/y(x),y(x))
\[y \left (x \right ) = -\frac {\sqrt {2}\, \sqrt {\left (\AiryAi \left (-\left (-8 i\right )^{\frac {1}{3}} x \right ) c_{1}+\AiryBi \left (-\left (-8 i\right )^{\frac {1}{3}} x \right )\right ) \left (\left (1+i \sqrt {3}\right ) c_{1} \AiryAi \left (1, -\left (-8 i\right )^{\frac {1}{3}} x \right )+\left (1+i \sqrt {3}\right ) \AiryBi \left (1, -\left (-8 i\right )^{\frac {1}{3}} x \right )-2 x^{2} \left (\AiryAi \left (-\left (-8 i\right )^{\frac {1}{3}} x \right ) c_{1}+\AiryBi \left (-\left (-8 i\right )^{\frac {1}{3}} x \right )\right )\right )}}{2 \AiryAi \left (-\left (-8 i\right )^{\frac {1}{3}} x \right ) c_{1}+2 \AiryBi \left (-\left (-8 i\right )^{\frac {1}{3}} x \right )}\]