3.743   ODE No. 743

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

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

Mathematica: cpu = 32.841170 (sec), leaf count = 43 \[ \text {DSolve}\left [y'(x)=-\frac {i \left (x^4+8 x^2 y(x)^2+16 y(x)^4+8 i x\right )}{32 y(x)},y(x),x\right ] \]

Maple: cpu = 0.328 (sec), leaf count = 269 \[ \left \{ y \left ( x \right ) ={-i\sqrt {-i \left ( -2\, \left ( -\sqrt {3 }+i \right ) {\it \_C1}\,{{\rm Ai}^{(1)}\left (-1/2\, \left ( \sqrt {3}-i \right ) x\right )}+ \left ( -2\,i+2\,\sqrt {3} \right ) {{\rm Bi}^{(1 )}\left (-{\frac { \left ( \sqrt {3}-i \right ) x}{2}}\right )}+i{x}^{2} \left ( {{\rm Ai}\left (-{\frac { \left ( \sqrt {3}-i \right ) x}{2}} \right )}{\it \_C1}+{{\rm Bi}\left (-{\frac { \left ( \sqrt {3}-i \right ) x}{2}}\right )} \right ) \right ) \left ( {{\rm Ai}\left (-{ \frac { \left ( \sqrt {3}-i \right ) x}{2}}\right )}{\it \_C1}+{{\rm Bi} \left (-{\frac { \left ( \sqrt {3}-i \right ) x}{2}}\right )} \right ) } \left ( 2\,{{\rm Ai}\left (-1/2\, \left ( \sqrt {3}-i \right ) x\right )}{ \it \_C1}+2\,{{\rm Bi}\left (-1/2\, \left ( \sqrt {3}-i \right ) x \right )} \right ) ^{-1}},y \left ( x \right ) ={i\sqrt {-i \left ( -2\, \left ( -\sqrt {3}+i \right ) {\it \_C1}\,{{\rm Ai}^{(1)}\left (-1/2\, \left ( \sqrt {3}-i \right ) x\right )}+ \left ( -2\,i+2\,\sqrt {3} \right ) {{\rm Bi}^{(1)}\left (-{\frac { \left ( \sqrt {3}-i \right ) x}{ 2}}\right )}+i{x}^{2} \left ( {{\rm Ai}\left (-{\frac { \left ( \sqrt {3}- i \right ) x}{2}}\right )}{\it \_C1}+{{\rm Bi}\left (-{\frac { \left ( \sqrt {3}-i \right ) x}{2}}\right )} \right ) \right ) \left ( {{\rm Ai} \left (-{\frac { \left ( \sqrt {3}-i \right ) x}{2}}\right )}{\it \_C1}+{ {\rm Bi}\left (-{\frac { \left ( \sqrt {3}-i \right ) x}{2}}\right )} \right ) } \left ( 2\,{{\rm Ai}\left (-1/2\, \left ( \sqrt {3}-i \right ) x\right )}{\it \_C1}+2\,{{\rm Bi}\left (-1/2\, \left ( \sqrt {3}-i \right ) x\right )} \right ) ^{-1}} \right \} \]