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 = 0.830027 (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 = 0.123 (sec), leaf count = 34

\[\left \{y \left (x \right ) = \left (c_{1} \cos \left (x \right )-\left (\int \frac {\sin \left (x \right )}{x \cos \left (x \right )}d x \right ) \cos \left (x \right )+\left (c_{2}+\ln \left (x \right )\right ) \sin \left (x \right )\right ) x\right \}\]