4.290   ODE No. 1290

\[ \boxed { \left ( 27\,{x}^{2}+4 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +27\,x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -3\,y \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.175022 (sec), leaf count = 103 \[ \left \{\left \{y(x)\to c_1 \cosh \left (\frac {\sqrt {-27 x^2-4} \tan ^{-1}\left (\frac {3 x}{\sqrt {-9 x^2-\frac {4}{3}}}\right )}{3 \sqrt {27 x^2+4}}\right )+i c_2 \sinh \left (\frac {\sqrt {-27 x^2-4} \tan ^{-1}\left (\frac {3 x}{\sqrt {-9 x^2-\frac {4}{3}}}\right )}{3 \sqrt {27 x^2+4}}\right )\right \}\right \} \]

Maple: cpu = 0.015 (sec), leaf count = 47 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sin \left ( {\frac {1}{3} \arctan \left ( 3\,{\frac {\sqrt {3}x}{\sqrt {-27\,{x}^{2}-4}}} \right ) } \right ) +{\it \_C2}\,\cos \left ( {\frac {1}{3}\arctan \left ( 3\,{\frac {\sqrt {3}x}{\sqrt {-27\,{x}^{2}-4}}} \right ) } \right ) \right \} \]