2.1177   ODE No. 1177

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

\[ \left (x^2+2\right ) y'(x)+x^2 y''(x)+x^2 (-\sec (x))-2 x y'(x)=0 \] Mathematica : cpu = 0.79137 (sec), leaf count = 141

\[\left \{\left \{y(x)\to \int _1^xe^{\frac {2}{K[1]}-K[1]} K[1]^2dK[1] \int _1^x\frac {e^{K[3]-\frac {2}{K[3]}} \sec (K[3])}{K[3]^2}dK[3]+\int _1^x-\frac {e^{K[2]-\frac {2}{K[2]}} \sec (K[2]) \int _1^{K[2]}e^{\frac {2}{K[1]}-K[1]} K[1]^2dK[1]}{K[2]^2}dK[2]+c_2 \int _1^xe^{\frac {2}{K[1]}-K[1]} K[1]^2dK[1]+c_1\right \}\right \}\] Maple : cpu = 0.278 (sec), leaf count = 34

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