2.1421   ODE No. 1421

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

\[ y''(x)=-a^2 n y(x) \sec ^2(a x) \left ((n-1) \sin ^2(a x)+\cos ^2(a x)\right )-a (n-1) \sin (2 a x) \sec ^2(a x) y'(x) \] Mathematica : cpu = 0.248482 (sec), leaf count = 67

\[\left \{\left \{y(x)\to c_1 e^{-\sqrt {-a^2} x} \cos ^{n-1}(a x)+\frac {c_2 e^{\sqrt {-a^2} x} \cos ^{n-1}(a x)}{2 \sqrt {-a^2}}\right \}\right \}\]

Maple : cpu = 0.076 (sec), leaf count = 27

\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( \cos \left ( ax \right ) \right ) ^{n}+{\it \_C2}\,\sin \left ( ax \right ) \left ( \cos \left ( ax \right ) \right ) ^{n-1} \right \} \]