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10.32   ODE No. 1887

{d2dt2x(t)=ax(t)+by(t),d2dt2y(t)=cx(t)+dy(t)}

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

Mathematica: cpu = 0.480061 (sec), leaf count = 5748 {{x(t)→e−a+d−a2−2da+d2+4bct2−a+d+a2−2da+d2+4bct2(ea+d−a2−2da+d2+4bct2a−ea+d+a2−2da+d2+4bct2a−e2a+d−a2−2da+d2+4bct+a+d+a2−2da+d2+4bct2a+ea+d−a2−2da+d2+4bct2+2a+d+a2−2da+d2+4bcta−dea+d−a2−2da+d2+4bct2+a2−2da+d2+4bcea+d−a2−2da+d2+4bct2+dea+d+a2−2da+d2+4bct2+a2−2da+d2+4bcea+d+a2−2da+d2+4bct2+de2a+d−a2−2da+d2+4bct+a+d+a2−2da+d2+4bct2+a2−2da+d2+4bce2a+d−a2−2da+d2+4bct+a+d+a2−2da+d2+4bct2−dea+d−a2−2da+d2+4bct2+2a+d+a2−2da+d2+4bct+a2−2da+d2+4bcea+d−a2−2da+d2+4bct2+2a+d+a2−2da+d2+4bct)c14a2−2da+d2+4bc+e−a+d−a2−2da+d2+4bct2−a+d+a2−2da+d2+4bct2(−a+d−a2−2da+d2+4bcea+d−a2−2da+d2+4bct2a+a+d+a2−2da+d2+4bcea+d+a2−2da+d2+4bct2a−a+d+a2−2da+d2+4bce2a+d−a2−2da+d2+4bct+a+d+a2−2da+d2+4bct2a+a+d−a2−2da+d2+4bcea+d−a2−2da+d2+4bct2+2a+d+a2−2da+d2+4bcta+da+d−a2−2da+d2+4bcea+d−a2−2da+d2+4bct2−a2−2da+d2+4bca+d−a2−2da+d2+4bcea+d−a2−2da+d2+4bct2−da+d+a2−2da+d2+4bcea+d+a2−2da+d2+4bct2−a2−2da+d2+4bca+d+a2−2da+d2+4bcea+d+a2−2da+d2+4bct2+da+d+a2−2da+d2+4bce2a+d−a2−2da+d2+4bct+a+d+a2−2da+d2+4bct2+a2−2da+d2+4bca+d+a2−2da+d2+4bce2a+d−a2−2da+d2+4bct+a+d+a2−2da+d2+4bct2−da+d−a2−2da+d2+4bcea+d−a2−2da+d2+4bct2+2a+d+a2−2da+d2+4bct+a2−2da+d2+4bca+d−a2−2da+d2+4bcea+d−a2−2da+d2+4bct2+2a+d+a2−2da+d2+4bct)c222a2−2da+d2+4bca+d−a2−2da+d2+4bca+d+a2−2da+d2+4bc−be−a+d−a2−2da+d2+4bct2−a+d+a2−2da+d2+4bct2(−ea+d−a2−2da+d2+4bct2+ea+d+a2−2da+d2+4bct2+e2a+d−a2−2da+d2+4bct+a+d+a2−2da+d2+4bct2−ea+d−a2−2da+d2+4bct2+2a+d+a2−2da+d2+4bct)c32a2−2da+d2+4bc+be−a+d−a2−2da+d2+4bct2−a+d+a2−2da+d2+4bct2(−ea+d−a2−2da+d2+4bct2a+d−a2−2da+d2+4bc+ea+d−a2−2da+d2+4bct2+2a+d+a2−2da+d2+4bcta+d−a2−2da+d2+4bc+a+d+a2−2da+d2+4bcea+d+a2−2da+d2+4bct2−a+d+a2−2da+d2+4bce2a+d−a2−2da+d2+4bct+a+d+a2−2da+d2+4bct2)c42a2−2da+d2+4bca+d−a2−2da+d2+4bca+d+a2−2da+d2+4bc,y(t)→−ce−a+d−a2−2da+d2+4bct2−a+d+a2−2da+d2+4bct2(−ea+d−a2−2da+d2+4bct2+ea+d+a2−2da+d2+4bct2+e2a+d−a2−2da+d2+4bct+a+d+a2−2da+d2+4bct2−ea+d−a2−2da+d2+4bct2+2a+d+a2−2da+d2+4bct)c12a2−2da+d2+4bc+ce−a+d−a2−2da+d2+4bct2−a+d+a2−2da+d2+4bct2(−ea+d−a2−2da+d2+4bct2a+d−a2−2da+d2+4bc+ea+d−a2−2da+d2+4bct2+2a+d+a2−2da+d2+4bcta+d−a2−2da+d2+4bc+a+d+a2−2da+d2+4bcea+d+a2−2da+d2+4bct2−a+d+a2−2da+d2+4bce2a+d−a2−2da+d2+4bct+a+d+a2−2da+d2+4bct2)c22a2−2da+d2+4bca+d−a2−2da+d2+4bca+d+a2−2da+d2+4bc+e−a+d−a2−2da+d2+4bct2−a+d+a2−2da+d2+4bct2(−ea+d−a2−2da+d2+4bct2a+ea+d+a2−2da+d2+4bct2a+e2a+d−a2−2da+d2+4bct+a+d+a2−2da+d2+4bct2a−ea+d−a2−2da+d2+4bct2+2a+d+a2−2da+d2+4bcta+dea+d−a2−2da+d2+4bct2+a2−2da+d2+4bcea+d−a2−2da+d2+4bct2−dea+d+a2−2da+d2+4bct2+a2−2da+d2+4bcea+d+a2−2da+d2+4bct2−de2a+d−a2−2da+d2+4bct+a+d+a2−2da+d2+4bct2+a2−2da+d2+4bce2a+d−a2−2da+d2+4bct+a+d+a2−2da+d2+4bct2+dea+d−a2−2da+d2+4bct2+2a+d+a2−2da+d2+4bct+a2−2da+d2+4bcea+d−a2−2da+d2+4bct2+2a+d+a2−2da+d2+4bct)c34a2−2da+d2+4bc+e−a+d−a2−2da+d2+4bct2−a+d+a2−2da+d2+4bct2(a+d−a2−2da+d2+4bcea+d−a2−2da+d2+4bct2a−a+d+a2−2da+d2+4bcea+d+a2−2da+d2+4bct2a+a+d+a2−2da+d2+4bce2a+d−a2−2da+d2+4bct+a+d+a2−2da+d2+4bct2a−a+d−a2−2da+d2+4bcea+d−a2−2da+d2+4bct2+2a+d+a2−2da+d2+4bcta−da+d−a2−2da+d2+4bcea+d−a2−2da+d2+4bct2−a2−2da+d2+4bca+d−a2−2da+d2+4bcea+d−a2−2da+d2+4bct2+da+d+a2−2da+d2+4bcea+d+a2−2da+d2+4bct2−a2−2da+d2+4bca+d+a2−2da+d2+4bcea+d+a2−2da+d2+4bct2−da+d+a2−2da+d2+4bce2a+d−a2−2da+d2+4bct+a+d+a2−2da+d2+4bct2+a2−2da+d2+4bca+d+a2−2da+d2+4bce2a+d−a2−2da+d2+4bct+a+d+a2−2da+d2+4bct2+da+d−a2−2da+d2+4bcea+d−a2−2da+d2+4bct2+2a+d+a2−2da+d2+4bct+a2−2da+d2+4bca+d−a2−2da+d2+4bcea+d−a2−2da+d2+4bct2+2a+d+a2−2da+d2+4bct)c422a2−2da+d2+4bca+d−a2−2da+d2+4bca+d+a2−2da+d2+4bc}}

Maple: cpu = 0.094 (sec), leaf count = 418 {{x(t)=_C1e−t2−2a2−2da+4bc+d2+2a+2d+_C2et2−2a2−2da+4bc+d2+2a+2d+_C3e−t22a2−2da+4bc+d2+2a+2d+_C4et22a2−2da+4bc+d2+2a+2d,y(t)=(d2b+1b(12a2−2da+4bc+d2−a2))_C4et22a2−2da+4bc+d2+2a+2d+(d2b+1b(12a2−2da+4bc+d2−a2))_C3e−t22a2−2da+4bc+d2+2a+2d+(d2b+1b(−12a2−2da+4bc+d2−a2))_C2et2−2a2−2da+4bc+d2+2a+2d+(d2b+1b(−12a2−2da+4bc+d2−a2))_C1e−t2−2a2−2da+4bc+d2+2a+2d}}

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