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2.1005   ODE No. 1005

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

−sin⁡(ax)sin⁡(bx)+y″(x)+y(x)=0 ✓ Mathematica : cpu = 0.518654 (sec), leaf count = 1163

{{y(x)→c1cos⁡(x)+c2sin⁡(x)+−cos⁡(x)cos⁡((a−b−1)x)a3+cos⁡(x)cos⁡((a−b+1)x)a3+cos⁡(x)cos⁡((a+b−1)x)a3−cos⁡(x)cos⁡((a+b+1)x)a3+sin⁡(x)sin⁡((a−b−1)x)a3+sin⁡(x)sin⁡((a−b+1)x)a3−sin⁡(x)sin⁡((a+b−1)x)a3−sin⁡(x)sin⁡((a+b+1)x)a3−bcos⁡(x)cos⁡((a−b−1)x)a2−cos⁡(x)cos⁡((a−b−1)x)a2+bcos⁡(x)cos⁡((a−b+1)x)a2−cos⁡(x)cos⁡((a−b+1)x)a2−bcos⁡(x)cos⁡((a+b−1)x)a2+cos⁡(x)cos⁡((a+b−1)x)a2+bcos⁡(x)cos⁡((a+b+1)x)a2+cos⁡(x)cos⁡((a+b+1)x)a2+bsin⁡(x)sin⁡((a−b−1)x)a2+sin⁡(x)sin⁡((a−b−1)x)a2+bsin⁡(x)sin⁡((a−b+1)x)a2−sin⁡(x)sin⁡((a−b+1)x)a2+bsin⁡(x)sin⁡((a+b−1)x)a2−sin⁡(x)sin⁡((a+b−1)x)a2+bsin⁡(x)sin⁡((a+b+1)x)a2+sin⁡(x)sin⁡((a+b+1)x)a2+b2cos⁡(x)cos⁡((a−b−1)x)a−2bcos⁡(x)cos⁡((a−b−1)x)a+cos⁡(x)cos⁡((a−b−1)x)a−b2cos⁡(x)cos⁡((a−b+1)x)a−2bcos⁡(x)cos⁡((a−b+1)x)a−cos⁡(x)cos⁡((a−b+1)x)a−b2cos⁡(x)cos⁡((a+b−1)x)a−2bcos⁡(x)cos⁡((a+b−1)x)a−cos⁡(x)cos⁡((a+b−1)x)a+b2cos⁡(x)cos⁡((a+b+1)x)a−2bcos⁡(x)cos⁡((a+b+1)x)a+cos⁡(x)cos⁡((a+b+1)x)a−b2sin⁡(x)sin⁡((a−b−1)x)a+2bsin⁡(x)sin⁡((a−b−1)x)a−sin⁡(x)sin⁡((a−b−1)x)a−b2sin⁡(x)sin⁡((a−b+1)x)a−2bsin⁡(x)sin⁡((a−b+1)x)a−sin⁡(x)sin⁡((a−b+1)x)a+b2sin⁡(x)sin⁡((a+b−1)x)a+2bsin⁡(x)sin⁡((a+b−1)x)a+sin⁡(x)sin⁡((a+b−1)x)a+b2sin⁡(x)sin⁡((a+b+1)x)a−2bsin⁡(x)sin⁡((a+b+1)x)a+sin⁡(x)sin⁡((a+b+1)x)a+b3cos⁡(x)cos⁡((a−b−1)x)−b2cos⁡(x)cos⁡((a−b−1)x)−bcos⁡(x)cos⁡((a−b−1)x)+cos⁡(x)cos⁡((a−b−1)x)−b3cos⁡(x)cos⁡((a−b+1)x)−b2cos⁡(x)cos⁡((a−b+1)x)+bcos⁡(x)cos⁡((a−b+1)x)+cos⁡(x)cos⁡((a−b+1)x)+b3cos⁡(x)cos⁡((a+b−1)x)+b2cos⁡(x)cos⁡((a+b−1)x)−bcos⁡(x)cos⁡((a+b−1)x)−cos⁡(x)cos⁡((a+b−1)x)−b3cos⁡(x)cos⁡((a+b+1)x)+b2cos⁡(x)cos⁡((a+b+1)x)+bcos⁡(x)cos⁡((a+b+1)x)−cos⁡(x)cos⁡((a+b+1)x)−b3sin⁡(x)sin⁡((a−b−1)x)+b2sin⁡(x)sin⁡((a−b−1)x)+bsin⁡(x)sin⁡((a−b−1)x)−sin⁡(x)sin⁡((a−b−1)x)−b3sin⁡(x)sin⁡((a−b+1)x)−b2sin⁡(x)sin⁡((a−b+1)x)+bsin⁡(x)sin⁡((a−b+1)x)+sin⁡(x)sin⁡((a−b+1)x)−b3sin⁡(x)sin⁡((a+b−1)x)−b2sin⁡(x)sin⁡((a+b−1)x)+bsin⁡(x)sin⁡((a+b−1)x)+sin⁡(x)sin⁡((a+b−1)x)−b3sin⁡(x)sin⁡((a+b+1)x)+b2sin⁡(x)sin⁡((a+b+1)x)+bsin⁡(x)sin⁡((a+b+1)x)−sin⁡(x)sin⁡((a+b+1)x)4(a−b−1)(a−b+1)(a+b−1)(a+b+1)}}

✓ Maple : cpu = 0.105 (sec), leaf count = 82

{y(x)=sin⁡(x)_C2+cos⁡(x)_C1+−(a+b+1)(a+b−1)cos⁡(x(a−b))+cos⁡((a+b)x)(a−b+1)(a−b−1)2a4+(−4b2−4)a2+2b4−4b2+2}

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