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11.19   ODE No. 1931

{addtx(t)=(b−c)y(t)z(t),bddty(t)=(c−a)z(t)x(t),cddtz(t)=(a−b)x(t)y(t)}

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

Mathematica: cpu = 6.037767 (sec), leaf count = 10101 {{x(t)→2b2a(a−c)c1sn(2aa−ccc2tbb−c−2aba−cc2tb−c−2aa−ccc2c3bb−c+2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1−2ba(a−c)cc1sn(2aa−ccc2tbb−c−2aba−cc2tb−c−2aa−ccc2c3bb−c+2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1a,y(t)→−2c1b2−2cc1b+c(2b2a(a−c)c1sn(2aa−ccc2tbb−c−2aba−cc2tb−c−2aa−ccc2c3bb−c+2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1−2ba(a−c)cc1sn(2aa−ccc2tbb−c−2aba−cc2tb−c−2aa−ccc2c3bb−c+2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1)2a−(2b2a(a−c)c1sn(2aa−ccc2tbb−c−2aba−cc2tb−c−2aa−ccc2c3bb−c+2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1−2ba(a−c)cc1sn(2aa−ccc2tbb−c−2aba−cc2tb−c−2aa−ccc2c3bb−c+2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1)2b2−bc,z(t)→−2c2c2+2bc2c−b(2b2a(a−c)c1sn(2aa−ccc2tbb−c−2aba−cc2tb−c−2aa−ccc2c3bb−c+2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1−2ba(a−c)cc1sn(2aa−ccc2tbb−c−2aba−cc2tb−c−2aa−ccc2c3bb−c+2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1)2a+(2b2a(a−c)c1sn(2aa−ccc2tbb−c−2aba−cc2tb−c−2aa−ccc2c3bb−c+2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1−2ba(a−c)cc1sn(2aa−ccc2tbb−c−2aba−cc2tb−c−2aa−ccc2c3bb−c+2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1)2b−cc},{x(t)→2b2a(a−c)c1sn(2aa−ccc2tbb−c−2aba−cc2tb−c−2aa−ccc2c3bb−c+2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1−2ba(a−c)cc1sn(2aa−ccc2tbb−c−2aba−cc2tb−c−2aa−ccc2c3bb−c+2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1a,y(t)→2c1b2−2cc1b+c(2b2a(a−c)c1sn(2aa−ccc2tbb−c−2aba−cc2tb−c−2aa−ccc2c3bb−c+2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1−2ba(a−c)cc1sn(2aa−ccc2tbb−c−2aba−cc2tb−c−2aa−ccc2c3bb−c+2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1)2a−(2b2a(a−c)c1sn(2aa−ccc2tbb−c−2aba−cc2tb−c−2aa−ccc2c3bb−c+2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1−2ba(a−c)cc1sn(2aa−ccc2tbb−c−2aba−cc2tb−c−2aa−ccc2c3bb−c+2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1)2b2−bc,z(t)→−−2c2c2+2bc2c−b(2b2a(a−c)c1sn(2aa−ccc2tbb−c−2aba−cc2tb−c−2aa−ccc2c3bb−c+2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1−2ba(a−c)cc1sn(2aa−ccc2tbb−c−2aba−cc2tb−c−2aa−ccc2c3bb−c+2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1)2a+(2b2a(a−c)c1sn(2aa−ccc2tbb−c−2aba−cc2tb−c−2aa−ccc2c3bb−c+2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1−2ba(a−c)cc1sn(2aa−ccc2tbb−c−2aba−cc2tb−c−2aa−ccc2c3bb−c+2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1)2b−cc},{x(t)→2b2a(a−c)c1sn(−2aa−ccc2tbb−c+2aba−cc2tb−c+2aa−ccc2c3bb−c−2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1−2ba(a−c)cc1sn(−2aa−ccc2tbb−c+2aba−cc2tb−c+2aa−ccc2c3bb−c−2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1a,y(t)→−2c1b2−2cc1b+c(2b2a(a−c)c1sn(−2aa−ccc2tbb−c+2aba−cc2tb−c+2aa−ccc2c3bb−c−2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1−2ba(a−c)cc1sn(−2aa−ccc2tbb−c+2aba−cc2tb−c+2aa−ccc2c3bb−c−2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1)2a−(2b2a(a−c)c1sn(−2aa−ccc2tbb−c+2aba−cc2tb−c+2aa−ccc2c3bb−c−2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1−2ba(a−c)cc1sn(−2aa−ccc2tbb−c+2aba−cc2tb−c+2aa−ccc2c3bb−c−2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1)2b2−bc,z(t)→−−2c2c2+2bc2c−b(2b2a(a−c)c1sn(−2aa−ccc2tbb−c+2aba−cc2tb−c+2aa−ccc2c3bb−c−2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1−2ba(a−c)cc1sn(−2aa−ccc2tbb−c+2aba−cc2tb−c+2aa−ccc2c3bb−c−2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1)2a+(2b2a(a−c)c1sn(−2aa−ccc2tbb−c+2aba−cc2tb−c+2aa−ccc2c3bb−c−2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1−2ba(a−c)cc1sn(−2aa−ccc2tbb−c+2aba−cc2tb−c+2aa−ccc2c3bb−c−2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1)2b−cc},{x(t)→2b2a(a−c)c1sn(−2aa−ccc2tbb−c+2aba−cc2tb−c+2aa−ccc2c3bb−c−2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1−2ba(a−c)cc1sn(−2aa−ccc2tbb−c+2aba−cc2tb−c+2aa−ccc2c3bb−c−2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1a,y(t)→2c1b2−2cc1b+c(2b2a(a−c)c1sn(−2aa−ccc2tbb−c+2aba−cc2tb−c+2aa−ccc2c3bb−c−2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1−2ba(a−c)cc1sn(−2aa−ccc2tbb−c+2aba−cc2tb−c+2aa−ccc2c3bb−c−2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1)2a−(2b2a(a−c)c1sn(−2aa−ccc2tbb−c+2aba−cc2tb−c+2aa−ccc2c3bb−c−2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1−2ba(a−c)cc1sn(−2aa−ccc2tbb−c+2aba−cc2tb−c+2aa−ccc2c3bb−c−2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1)2b2−bc,z(t)→−2c2c2+2bc2c−b(2b2a(a−c)c1sn(−2aa−ccc2tbb−c+2aba−cc2tb−c+2aa−ccc2c3bb−c−2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1−2ba(a−c)cc1sn(−2aa−ccc2tbb−c+2aba−cc2tb−c+2aa−ccc2c3bb−c−2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1)2a+(2b2a(a−c)c1sn(−2aa−ccc2tbb−c+2aba−cc2tb−c+2aa−ccc2c3bb−c−2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1−2ba(a−c)cc1sn(−2aa−ccc2tbb−c+2aba−cc2tb−c+2aa−ccc2c3bb−c−2aba−cc2c3b−ca|−(a−b)bc1(a−c)cc2)(a−c)b(b−c)c1)2b−cc}}

Maple: cpu = 0.514 (sec), leaf count = 1356 {[{x(t)=0},{y(t)=0},{z(t)=_C1}],[{x(t)=0},{y(t)=_C1},{z(t)=0}],[{x(t)=_C1},{y(t)=0},{z(t)=0}],[{x(t)=RootOf(−∫_Z−2bc(a2−ab−ac+bc)bc(a2−ab−ac+bc)(−4_a4a4+8_a4a3b+8_a4a3c−4_a4a2b2−16_a4a2bc−4_a4a2c2+8_a4ab2c+8_a4abc2−4_a4b2c2+16_C2_a2a4−32_C2_a2a3b−32_C2_a2a3c+16_C2_a2a2b2+64_C2_a2a2bc+16_C2_a2a2c2−32_C2_a2ab2c−32_C2_a2abc2+16_C2_a2b2c2−16_C22a4+32_C22a3b+32_C22a3c−16_C22a2b2−64_C22a2bc−16_C22a2c2+32_C22ab2c+32_C22abc2−16_C22b2c2+_C1bc)d_a+t+_C3),x(t)=RootOf(−∫_Z2bc(a2−ab−ac+bc)bc(a2−ab−ac+bc)(−4_a4a4+8_a4a3b+8_a4a3c−4_a4a2b2−16_a4a2bc−4_a4a2c2+8_a4ab2c+8_a4abc2−4_a4b2c2+16_C2_a2a4−32_C2_a2a3b−32_C2_a2a3c+16_C2_a2a2b2+64_C2_a2a2bc+16_C2_a2a2c2−32_C2_a2ab2c−32_C2_a2abc2+16_C2_a2b2c2−16_C22a4+32_C22a3b+32_C22a3c−16_C22a2b2−64_C22a2bc−16_C22a2c2+32_C22ab2c+32_C22abc2−16_C22b2c2+_C1bc)d_a+t+_C3)},{y(t)=−22bx(t)(ab−ac−b2+bc)x(t)b(ab−ac−b2+bc)((d2dt2x(t))cb−4(x(t))2(ddtx(t))2a2bc−4(x(t))2(ddtx(t))2ab2c−4(x(t))2(ddtx(t))2abc2+4(x(t))2(ddtx(t))2b2c2+(d2dt2x(t))2b2c2)a,y(t)=22bx(t)(ab−ac−b2+bc)x(t)b(ab−ac−b2+bc)((d2dt2x(t))cb−4(x(t))2(ddtx(t))2a2bc−4(x(t))2(ddtx(t))2ab2c−4(x(t))2(ddtx(t))2abc2+4(x(t))2(ddtx(t))2b2c2+(d2dt2x(t))2b2c2)a,y(t)=−22bx(t)(ab−ac−b2+bc)x(t)b(ab−ac−b2+bc)((d2dt2x(t))cb+4(x(t))2(ddtx(t))2a2bc−4(x(t))2(ddtx(t))2ab2c−4(x(t))2(ddtx(t))2abc2+4(x(t))2(ddtx(t))2b2c2+(d2dt2x(t))2b2c2)a,y(t)=22bx(t)(ab−ac−b2+bc)x(t)b(ab−ac−b2+bc)((d2dt2x(t))cb+4(x(t))2(ddtx(t))2a2bc−4(x(t))2(ddtx(t))2ab2c−4(x(t))2(ddtx(t))2abc2+4(x(t))2(ddtx(t))2b2c2+(d2dt2x(t))2b2c2)a},{z(t)=addtx(t)by(t)−cy(t)}]}

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