2.759   ODE No. 759

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

\[ y'(x)=-\frac {i x \left (x^8+18 x^4 y(x)^2+54 i x^2+81 y(x)^4\right )}{243 y(x)} \] Mathematica : cpu = 40.7893 (sec), leaf count = 0 , could not solve

DSolve[Derivative[1][y][x] == ((-I/243)*x*((54*I)*x^2 + x^8 + 18*x^4*y[x]^2 + 81*y[x]^4))/y[x], y[x], x]

Maple : cpu = 0.704 (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 ( \left ( -27-27\,i- \left ( 1-i \right ) {x}^{6} \right ) {\it \_C1}\,{{\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 ( \left ( -27-27\,i- \left ( 1-i \right ) {x}^{6} \right ) {\it \_C1}\,{{\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 \} \]