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2.1931   ODE No. 1931

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

{ax′(t)=(b−c)y(t)z(t),by′(t)=(c−a)x(t)z(t),cz′(t)=(a−b)x(t)y(t)} ✓ Mathematica : cpu = 5.51259 (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 = 0.627 (sec), leaf count = 944

{[{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(RootOf(−_a2−2∫_Z−4_C12_h2a2bc+4_C12_h2ab2c+4_C12_h2abc2−4_C12_h2b2c2+_C1bc_h4_C1_h2a2−4_C1_h2ab−4_C1_h2ac+4_C1_h2bc−1d_h+2_C2))−1d_a+t+_C3),x(t)=RootOf(−∫_Z(RootOf(−_a2+2∫_Z−4_C12_h2a2bc+4_C12_h2ab2c+4_C12_h2abc2−4_C12_h2b2c2+_C1bc_h4_C1_h2a2−4_C1_h2ab−4_C1_h2ac+4_C1_h2bc−1d_h+2_C2))−1d_a+t+_C3)},{y(t)=−12bx(t)(ab−ac−b2+bc)−2x(t)b(ab−ac−b2+bc)(−(d2dt2x(t))bc+4(ddtx(t))2(x(t))2a2bc−4(ddtx(t))2(x(t))2ab2c−4(ddtx(t))2(x(t))2abc2+4(ddtx(t))2(x(t))2b2c2+(d2dt2x(t))2b2c2)a,y(t)=12bx(t)(ab−ac−b2+bc)−2x(t)b(ab−ac−b2+bc)(−(d2dt2x(t))bc+4(ddtx(t))2(x(t))2a2bc−4(ddtx(t))2(x(t))2ab2c−4(ddtx(t))2(x(t))2abc2+4(ddtx(t))2(x(t))2b2c2+(d2dt2x(t))2b2c2)a,y(t)=−22bx(t)(ab−ac−b2+bc)x(t)b(ab−ac−b2+bc)((d2dt2x(t))bc+4(ddtx(t))2(x(t))2a2bc−4(ddtx(t))2(x(t))2ab2c−4(ddtx(t))2(x(t))2abc2+4(ddtx(t))2(x(t))2b2c2+(d2dt2x(t))2b2c2)a,y(t)=22bx(t)(ab−ac−b2+bc)x(t)b(ab−ac−b2+bc)((d2dt2x(t))bc+4(ddtx(t))2(x(t))2a2bc−4(ddtx(t))2(x(t))2ab2c−4(ddtx(t))2(x(t))2abc2+4(ddtx(t))2(x(t))2b2c2+(d2dt2x(t))2b2c2)a},{z(t)=addtx(t)by(t)−cy(t)}]}

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