4.433   ODE No. 1433

\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-{\frac {\sin \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{\cos \left ( x \right ) }}-1/4\,{\frac { \left ( 2\,{x}^{2}+{x}^{2} \left ( \sin \left ( x \right ) \right ) ^{2}-24\, \left ( \cos \left ( x \right ) \right ) ^{2} \right ) y \left ( x \right ) }{{x}^{2} \left ( \cos \left ( x \right ) \right ) ^{2}}}+\sqrt {\cos \left ( x \right ) }=0} \]

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

Mathematica: cpu = 0.200525 (sec), leaf count = 46 \[ \left \{\left \{y(x)\to \frac {1}{5} c_2 x^3 \sqrt {\cos (x)}+\frac {c_1 \sqrt {\cos (x)}}{x^2}-\frac {1}{4} x^2 \sqrt {\cos (x)}\right \}\right \} \]

Maple: cpu = 0.078 (sec), leaf count = 32 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C2}}{{x}^{2}}\sqrt {\cos \left ( x \right ) }}+\sqrt {\cos \left ( x \right ) }{x}^{3}{\it \_C1}-{ \frac {{x}^{2}}{4}\sqrt {\cos \left ( x \right ) }} \right \} \]