ODE No. 1504

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

\[ \left (x^2+2\right ) y^{(3)}(x)+\left (x^2+2\right ) y'(x)-2 x y''(x)-2 x y(x)=0 \] Mathematica : cpu = 1.24827 (sec), leaf count = 85

\[\left \{\left \{y(x)\to \frac {c_1 x^2}{2}-\frac {i c_2 e^{i x} \sqrt {\frac {4}{x^2}+1} x}{2 \sqrt {x^2+4}}-\frac {c_3 e^{-i x} \sqrt {\frac {4}{x^2}+1} x}{4 \sqrt {x^2+4}}\right \}\right \}\] Maple : cpu = 0.21 (sec), leaf count = 18

\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{2}+{\it \_C2}\,\cos \left ( x \right ) +{\it \_C3}\,\sin \left ( x \right ) \right \} \]