2.1177   ODE No. 1177

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

\[ x^2 y''(x)+\left (x^2+2\right ) y'(x)+x^2 (-\sec (x))-2 x y'(x)=0 \] Mathematica : cpu = 518.733 (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 = 0.076 (sec), leaf count = 39

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