2.1418   ODE No. 1418

\[ y''(x)=\frac {y(x) \sin (x)}{x \cos (x)-\sin (x)}-\frac {x \sin (x) y'(x)}{x \cos (x)-\sin (x)} \] Mathematica : cpu = 0.115556 (sec), leaf count = 15


\[\{\{y(x)\to c_1 x+c_2 \sin (x)\}\}\] Maple : cpu = 4.603 (sec), leaf count = 59


\[y \relax (x ) = \sin \relax (x ) \left (\left (\int {\mathrm e}^{\int \frac {-2 \left (\cos ^{3}\relax (x )\right ) x +3 \left (\cos ^{2}\relax (x )\right ) \sin \relax (x )-\sin \relax (x )}{\cos \relax (x ) \left (\cos \relax (x ) x -\sin \relax (x )\right ) \sin \relax (x )}d x} \cos \relax (x )d x \right ) c_{2}+c_{1}\right )\]