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3.532   ODE No. 532

a(ddxy(x))3+b(ddxy(x))2+cddxy(x)−y(x)−d=0

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

Mathematica: cpu = 3505.56 (sec), leaf count = 1258 {{y(x)→InverseFunction[∫1#12b3−9acb−27a2d−27a2K[1]+4(3ac−b2)3+(2b3−9acb−27a2d−27a2K[1])232b2b3−9acb−27a2d−27a2K[1]+4(3ac−b2)3+(2b3−9acb−27a2d−27a2K[1])23+22/3(2b3−9acb−27a2d−27a2K[1]+4(3ac−b2)3+(2b3−9acb−27a2d−27a2K[1])2)2/3+223b2−623acdK[1]&][c1−x6a]},{y(x)→InverseFunction[∫1#12b3−9acb−27a2d−27a2K[2]+4(3ac−b2)3+(2b3−9acb−27a2d−27a2K[2])23−4b2b3−9acb−27a2d−27a2K[2]+4(3ac−b2)3+(2b3−9acb−27a2d−27a2K[2])23+22/3(2b3−9acb−27a2d−27a2K[2]+4(3ac−b2)3+(2b3−9acb−27a2d−27a2K[2])2)2/3−i22/33(2b3−9acb−27a2d−27a2K[2]+4(3ac−b2)3+(2b3−9acb−27a2d−27a2K[2])2)2/3+223b2−623ac−6i233ac+2233b2idK[2]&][x12a+c1]},{y(x)→InverseFunction[∫1#12b3−9acb−27a2d−27a2K[3]+4(3ac−b2)3+(2b3−9acb−27a2d−27a2K[3])23−4b2b3−9acb−27a2d−27a2K[3]+4(3ac−b2)3+(2b3−9acb−27a2d−27a2K[3])23+22/3(2b3−9acb−27a2d−27a2K[3]+4(3ac−b2)3+(2b3−9acb−27a2d−27a2K[3])2)2/3+22/33i(2b3−9acb−27a2d−27a2K[3]+4(3ac−b2)3+(2b3−9acb−27a2d−27a2K[3])2)2/3+223b2−2i233b2−623ac+6233acidK[3]&][x12a+c1]}}

Maple: cpu = 0.125 (sec), leaf count = 1211 {x−∫y(x)6a108_aa2+12327_a2a2+54_aa2d+18_aabc−4_ab3+27a2d2+18abcd+4ac3−4b3d−b2c2a+108a2d+36abc−8b33(108_aa2+12327_a2a2+54_aa2d+18_aabc−4_ab3+27a2d2+18abcd+4ac3−4b3d−b2c2a+108a2d+36abc−8b3)2/3−2b108_aa2+12327_a2a2+54_aa2d+18_aabc−4_ab3+27a2d2+18abcd+4ac3−4b3d−b2c2a+108a2d+36abc−8b33−12ac+4b2d_a−_C1=0,x−∫y(x)12a108_aa2+12327_a2a2+54_aa2d+18_aabc−4_ab3+27a2d2+18abcd+4ac3−4b3d−b2c2a+108a2d+36abc−8b33(i3−1)(i108_aa2+12327_a2a2+54_aa2d+18_aabc−4_ab3+27a2d2+18abcd+4ac3−4b3d−b2c2a+108a2d+36abc−8b333b−6i3ac+2i3b2+(108_aa2+12327_a2a2+54_aa2d+18_aabc−4_ab3+27a2d2+18abcd+4ac3−4b3d−b2c2a+108a2d+36abc−8b3)2/3+b108_aa2+12327_a2a2+54_aa2d+18_aabc−4_ab3+27a2d2+18abcd+4ac3−4b3d−b2c2a+108a2d+36abc−8b33+6ac−2b2)d_a−_C1=0,x−∫y(x)12a108_aa2+12327_a2a2+54_aa2d+18_aabc−4_ab3+27a2d2+18abcd+4ac3−4b3d−b2c2a+108a2d+36abc−8b33(i3+1)(i108_aa2+12327_a2a2+54_aa2d+18_aabc−4_ab3+27a2d2+18abcd+4ac3−4b3d−b2c2a+108a2d+36abc−8b333b−6i3ac+2i3b2−(108_aa2+12327_a2a2+54_aa2d+18_aabc−4_ab3+27a2d2+18abcd+4ac3−4b3d−b2c2a+108a2d+36abc−8b3)2/3−b108_aa2+12327_a2a2+54_aa2d+18_aabc−4_ab3+27a2d2+18abcd+4ac3−4b3d−b2c2a+108a2d+36abc−8b33−6ac+2b2)d_a−_C1=0}

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