3.769   ODE No. 769

\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {-i/32 \left ( 16\,i{x}^{2}+16\, \left ( y \left ( x \right ) \right ) ^{4}+8\,{x}^{4} \left ( y \left ( x \right ) \right ) ^{2}+{x}^{8} \right ) x}{y \left ( x \right ) }}=0} \]

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

Mathematica: cpu = 42.445390 (sec), leaf count = 46 \[ \text {DSolve}\left [y'(x)=-\frac {i x \left (x^8+8 x^4 y(x)^2+16 i x^2+16 y(x)^4\right )}{32 y(x)},y(x),x\right ] \]

Maple: cpu = 0.359 (sec), leaf count = 251 \[ \left \{ y \left ( x \right ) =-{\frac {\sqrt {4}}{2\,x}\sqrt { \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 ( { {\sl J}_{{\frac {4}{3}}}\left ( \left ( {\frac {1}{3}}-{\frac {i}{3}} \right ) {x}^{3}\right )}{\it \_C1}+{{\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 ) } \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 ( -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 ( {{\sl J}_{{\frac {4}{3}}}\left ( \left ( { \frac {1}{3}}-{\frac {i}{3}} \right ) {x}^{3}\right )}{\it \_C1}+{ {\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 ) } \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 \} \]