4.177   ODE No. 1177

\[ \boxed { {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -2\,x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( {x}^{2}+2 \right ) y \left ( x \right ) -{\frac {{x}^{2}}{\cos \left ( x \right ) }}=0} \]

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

Mathematica: cpu = 174.646177 (sec), leaf count = 136 \[ \left \{\left \{y(x)\to c_2 \int _1^x e^{\frac {2}{K[1]}-K[1]} K[1]^2 \, dK[1]+\int _1^x -\frac {e^{K[2]-\frac {2}{K[2]}} \sec (K[2]) \left (\int _1^{K[2]} e^{\frac {2}{K[1]}-K[1]} K[1]^2 \, dK[1]\right )}{K[2]^2} \, dK[2]+\left (\int _1^x e^{\frac {2}{K[1]}-K[1]} K[1]^2 \, dK[1]\right ) \int _1^x \frac {e^{K[3]-\frac {2}{K[3]}} \sec (K[3])}{K[3]^2} \, dK[3]+c_1\right \}\right \} \]

Maple: cpu = 0.062 (sec), leaf count = 39 \[ \left \{ y \left ( x \right ) =x\sin \left ( x \right ) {\it \_C2}+\cos \left ( x \right ) x{\it \_C1}+x \left ( \ln \left ( x \right ) \sin \left ( x \right ) -\int \!{\frac {\sin \left ( x \right ) }{\cos \left ( x \right ) x}}\,{\rm d}x\cos \left ( x \right ) \right ) \right \} \]