3.759   ODE No. 759

\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {-{\frac {i}{243}} \left ( 54\,i{x}^{2}+81\, \left ( y \left ( x \right ) \right ) ^{4}+18\,{x}^{4} \left ( y \left ( x \right ) \right ) ^{2}+{x}^{8} \right ) x}{y \left ( x \right ) }}=0} \]

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

Mathematica: cpu = 40.967202 (sec), leaf count = 46 \[ \text {DSolve}\left [y'(x)=-\frac {i x \left (x^8+18 x^4 y(x)^2+54 i x^2+81 y(x)^4\right )}{243 y(x)},y(x),x\right ] \]

Maple: cpu = 0.452 (sec), leaf count = 315 \[ \left \{ y \left ( x \right ) ={\frac {-{\frac {1}{6}}-{\frac {i}{6}}}{x }\sqrt { \left ( 1-i \right ) \left ( {{\sl J}_{{\frac {1}{3}}}\left ( \left ( {\frac {2}{27}}-{\frac {2\,i}{27}} \right ) \sqrt {6}{x}^{3} \right )}{\it \_C1}+{{\sl Y}_{{\frac {1}{3}}}\left ( \left ( {\frac {2}{ 27}}-{\frac {2\,i}{27}} \right ) \sqrt {6}{x}^{3}\right )} \right ) \left ( {\it \_C1}\, \left ( -27-27\,i- \left ( 1-i \right ) {x}^{6} \right ) {{\sl J}_{{\frac {1}{3}}}\left ( \left ( {\frac {2}{27}}-{ \frac {2\,i}{27}} \right ) \sqrt {6}{x}^{3}\right )}+ \left ( -27-27\,i- \left ( 1-i \right ) {x}^{6} \right ) {{\sl Y}_{{\frac {1}{3}}}\left ( \left ( {\frac {2}{27}}-{\frac {2\,i}{27}} \right ) \sqrt {6}{x}^{3} \right )}+6\,{x}^{3}\sqrt {6} \left ( {{\sl J}_{4/3}\left ( \left ( { \frac {2}{27}}-{\frac {2\,i}{27}} \right ) \sqrt {6}{x}^{3}\right )}{ \it \_C1}+{{\sl Y}_{4/3}\left ( \left ( {\frac {2}{27}}-{\frac {2\,i}{27 }} \right ) \sqrt {6}{x}^{3}\right )} \right ) \right ) } \left ( {{\sl J} _{{\frac {1}{3}}}\left ( \left ( {\frac {2}{27}}-{\frac {2\,i}{27}} \right ) \sqrt {6}{x}^{3}\right )}{\it \_C1}+{{\sl Y}_{{\frac {1}{3}} }\left ( \left ( {\frac {2}{27}}-{\frac {2\,i}{27}} \right ) \sqrt {6}{x} ^{3}\right )} \right ) ^{-1}},y \left ( x \right ) ={\frac {{\frac {1}{6}} +{\frac {i}{6}}}{x}\sqrt { \left ( 1-i \right ) \left ( {{\sl J}_{{ \frac {1}{3}}}\left ( \left ( {\frac {2}{27}}-{\frac {2\,i}{27}} \right ) \sqrt {6}{x}^{3}\right )}{\it \_C1}+{{\sl Y}_{{\frac {1}{3}} }\left ( \left ( {\frac {2}{27}}-{\frac {2\,i}{27}} \right ) \sqrt {6}{x} ^{3}\right )} \right ) \left ( {\it \_C1}\, \left ( -27-27\,i- \left ( 1-i \right ) {x}^{6} \right ) {{\sl J}_{{\frac {1}{3}}}\left ( \left ( { \frac {2}{27}}-{\frac {2\,i}{27}} \right ) \sqrt {6}{x}^{3}\right )}+ \left ( -27-27\,i- \left ( 1-i \right ) {x}^{6} \right ) {{\sl Y}_{{ \frac {1}{3}}}\left ( \left ( {\frac {2}{27}}-{\frac {2\,i}{27}} \right ) \sqrt {6}{x}^{3}\right )}+6\,{x}^{3}\sqrt {6} \left ( {{\sl J} _{4/3}\left ( \left ( {\frac {2}{27}}-{\frac {2\,i}{27}} \right ) \sqrt { 6}{x}^{3}\right )}{\it \_C1}+{{\sl Y}_{4/3}\left ( \left ( {\frac {2}{27} }-{\frac {2\,i}{27}} \right ) \sqrt {6}{x}^{3}\right )} \right ) \right ) } \left ( {{\sl J}_{{\frac {1}{3}}}\left ( \left ( {\frac {2}{27 }}-{\frac {2\,i}{27}} \right ) \sqrt {6}{x}^{3}\right )}{\it \_C1}+{ {\sl Y}_{{\frac {1}{3}}}\left ( \left ( {\frac {2}{27}}-{\frac {2\,i}{27 }} \right ) \sqrt {6}{x}^{3}\right )} \right ) ^{-1}} \right \} \]