#### 2.769   ODE No. 769

$y'(x)=-\frac {i x \left (x^8+8 x^4 y(x)^2+16 i x^2+16 y(x)^4\right )}{32 y(x)}$ Mathematica : cpu = 42.1802 (sec), leaf count = 0 , could not solve

DSolve[Derivative[1][y][x] == ((-I/32)*x*((16*I)*x^2 + x^8 + 8*x^4*y[x]^2 + 16*y[x]^4))/y[x], y[x], x]

Maple : cpu = 0.296 (sec), leaf count = 251

$\left \{ y \left ( x \right ) =-{\frac {\sqrt {4}}{2\,x}\sqrt { \left ( {{\sl J}_{{\frac {1}{3}}}\left ( \left ( {\frac {1}{3}}-{\frac {i}{3}} \right ) {x}^{3}\right )}{\it \_C1}+{{\sl Y}_{{\frac {1}{3}}}\left ( \left ( {\frac {1}{3}}-{\frac {i}{3}} \right ) {x}^{3}\right )} \right ) \left ( -2\, \left ( 1/8\,{x}^{6}+i \right ) {\it \_C1}\,{{\sl J}_{1/3}\left ( \left ( 1/3-i/3 \right ) {x}^{3}\right )}+ \left ( -{\frac {{x}^{6}}{4}}-2\,i \right ) {{\sl Y}_{{\frac {1}{3}}}\left ( \left ( {\frac {1}{3}}-{\frac {i}{3}} \right ) {x}^{3}\right )}+ \left ( 1+i \right ) \left ( {\it \_C1}\,{{\sl J}_{{\frac {4}{3}}}\left ( \left ( {\frac {1}{3}}-{\frac {i}{3}} \right ) {x}^{3}\right )}+{{\sl Y}_{{\frac {4}{3}}}\left ( \left ( {\frac {1}{3}}-{\frac {i}{3}} \right ) {x}^{3}\right )} \right ) {x}^{3} \right ) } \left ( {{\sl J}_{{\frac {1}{3}}}\left ( \left ( {\frac {1}{3}}-{\frac {i}{3}} \right ) {x}^{3}\right )}{\it \_C1}+{{\sl Y}_{{\frac {1}{3}}}\left ( \left ( {\frac {1}{3}}-{\frac {i}{3}} \right ) {x}^{3}\right )} \right ) ^{-1}},y \left ( x \right ) ={\frac {\sqrt {4}}{2\,x}\sqrt { \left ( {{\sl J}_{{\frac {1}{3}}}\left ( \left ( {\frac {1}{3}}-{\frac {i}{3}} \right ) {x}^{3}\right )}{\it \_C1}+{{\sl Y}_{{\frac {1}{3}}}\left ( \left ( {\frac {1}{3}}-{\frac {i}{3}} \right ) {x}^{3}\right )} \right ) \left ( -2\, \left ( 1/8\,{x}^{6}+i \right ) {\it \_C1}\,{{\sl J}_{1/3}\left ( \left ( 1/3-i/3 \right ) {x}^{3}\right )}+ \left ( -{\frac {{x}^{6}}{4}}-2\,i \right ) {{\sl Y}_{{\frac {1}{3}}}\left ( \left ( {\frac {1}{3}}-{\frac {i}{3}} \right ) {x}^{3}\right )}+ \left ( 1+i \right ) \left ( {\it \_C1}\,{{\sl J}_{{\frac {4}{3}}}\left ( \left ( {\frac {1}{3}}-{\frac {i}{3}} \right ) {x}^{3}\right )}+{{\sl Y}_{{\frac {4}{3}}}\left ( \left ( {\frac {1}{3}}-{\frac {i}{3}} \right ) {x}^{3}\right )} \right ) {x}^{3} \right ) } \left ( {{\sl J}_{{\frac {1}{3}}}\left ( \left ( {\frac {1}{3}}-{\frac {i}{3}} \right ) {x}^{3}\right )}{\it \_C1}+{{\sl Y}_{{\frac {1}{3}}}\left ( \left ( {\frac {1}{3}}-{\frac {i}{3}} \right ) {x}^{3}\right )} \right ) ^{-1}} \right \}$