ODE No. 1418

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

\[ y''(x)=\frac {y(x) \sin (x)}{x \cos (x)-\sin (x)}-\frac {x \sin (x) y'(x)}{x \cos (x)-\sin (x)} \] Mathematica : cpu = 1.26402 (sec), leaf count = 0 , could not solve

DSolve[Derivative[2][y][x] == (Sin[x]*y[x])/(x*Cos[x] - Sin[x]) - (x*Sin[x]*Derivative[1][y][x])/(x*Cos[x] - Sin[x]), y[x], x]

Maple : cpu = 3.699 (sec), leaf count = 59

\[ \left \{ y \left ( x \right ) =\sin \left ( x \right ) \left ( \int \!{{\rm e}^{\int \!{\frac {-2\, \left ( \cos \left ( x \right ) \right ) ^{3}x+3\, \left ( \cos \left ( x \right ) \right ) ^{2}\sin \left ( x \right ) -\sin \left ( x \right ) }{\cos \left ( x \right ) \left ( \cos \left ( x \right ) x-\sin \left ( x \right ) \right ) \sin \left ( x \right ) }}\,{\rm d}x}}\cos \left ( x \right ) \,{\rm d}x{\it \_C2}+{\it \_C1} \right ) \right \} \]