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3.252   ODE No. 252

(x2y(x)−1)ddxy(x)−x(y(x))2+1=0

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

Mathematica: cpu = 7.835995 (sec), leaf count = 819 {{y(x)→6xc1−x6c1−1+−1944c12x3+648c1x3−54x3+1944c12−648c1+4(54x2c1−9x2)3+(−1944c12x3+648c1x3−54x3+1944c12−648c1+54)2+543323(6c1−1)−23(54x2c1−9x2)3(6c1−1)−1944c12x3+648c1x3−54x3+1944c12−648c1+4(54x2c1−9x2)3+(−1944c12x3+648c1x3−54x3+1944c12−648c1+54)2+543},{y(x)→6xc1−x6c1−1−(1−i3)−1944c12x3+648c1x3−54x3+1944c12−648c1+4(54x2c1−9x2)3+(−1944c12x3+648c1x3−54x3+1944c12−648c1+54)2+543623(6c1−1)+(1+i3)(54x2c1−9x2)3 22/3(6c1−1)−1944c12x3+648c1x3−54x3+1944c12−648c1+4(54x2c1−9x2)3+(−1944c12x3+648c1x3−54x3+1944c12−648c1+54)2+543},{y(x)→6xc1−x6c1−1−(1+i3)−1944c12x3+648c1x3−54x3+1944c12−648c1+4(54x2c1−9x2)3+(−1944c12x3+648c1x3−54x3+1944c12−648c1+54)2+543623(6c1−1)+(1−i3)(54x2c1−9x2)3 22/3(6c1−1)−1944c12x3+648c1x3−54x3+1944c12−648c1+4(54x2c1−9x2)3+(−1944c12x3+648c1x3−54x3+1944c12−648c1+54)2+543}}

Maple: cpu = 0.562 (sec), leaf count = 1623 {y(x)=−14x2(63x3−63x2_C1x6−80x6+160x3−80_C1(−1+4−5x6−10x3+5_C1x6−80x6+160x3−80)(_C1x6−80x6+160x3−80)23−63_C1x41_C1(−1+4−5x6−10x3+5_C1x6−80x6+160x3−80)(_C1x6−80x6+160x3−80)23)(63x24_C1x6−320x6+640x3−320_C1(−1+4−5x6−10x3+5_C1x6−80x6+160x3−80)(_C1x6−80x6+160x3−80)23+63_C1x441_C1(−1+4−5x6−10x3+5_C1x6−80x6+160x3−80)(_C1x6−80x6+160x3−80)23−634)−1,y(x)=−14x2(63x3+63x22_C1x6−160x6+320x3−160_C1(−1+4−5x6−10x3+5_C1x6−80x6+160x3−80)(_C1x6−80x6+160x3−80)23+63_C1x421_C1(−1+4−5x6−10x3+5_C1x6−80x6+160x3−80)(_C1x6−80x6+160x3−80)23−2i3(63x24_C1x6−320x6+640x3−320_C1(−1+4−5x6−10x3+5_C1x6−80x6+160x3−80)(_C1x6−80x6+160x3−80)23−63_C1x441_C1(−1+4−5x6−10x3+5_C1x6−80x6+160x3−80)(_C1x6−80x6+160x3−80)23))(−63x28_C1x6−640x6+1280x3−640_C1(−1+4−5x6−10x3+5_C1x6−80x6+160x3−80)(_C1x6−80x6+160x3−80)23−63_C1x481_C1(−1+4−5x6−10x3+5_C1x6−80x6+160x3−80)(_C1x6−80x6+160x3−80)23−634+i23(63x24_C1x6−320x6+640x3−320_C1(−1+4−5x6−10x3+5_C1x6−80x6+160x3−80)(_C1x6−80x6+160x3−80)23−63_C1x441_C1(−1+4−5x6−10x3+5_C1x6−80x6+160x3−80)(_C1x6−80x6+160x3−80)23))−1,y(x)=−14x2(63x3+63x22_C1x6−160x6+320x3−160_C1(−1+4−5x6−10x3+5_C1x6−80x6+160x3−80)(_C1x6−80x6+160x3−80)23+63_C1x421_C1(−1+4−5x6−10x3+5_C1x6−80x6+160x3−80)(_C1x6−80x6+160x3−80)23+2i3(63x24_C1x6−320x6+640x3−320_C1(−1+4−5x6−10x3+5_C1x6−80x6+160x3−80)(_C1x6−80x6+160x3−80)23−63_C1x441_C1(−1+4−5x6−10x3+5_C1x6−80x6+160x3−80)(_C1x6−80x6+160x3−80)23))(−63x28_C1x6−640x6+1280x3−640_C1(−1+4−5x6−10x3+5_C1x6−80x6+160x3−80)(_C1x6−80x6+160x3−80)23−63_C1x481_C1(−1+4−5x6−10x3+5_C1x6−80x6+160x3−80)(_C1x6−80x6+160x3−80)23−634−i23(63x24_C1x6−320x6+640x3−320_C1(−1+4−5x6−10x3+5_C1x6−80x6+160x3−80)(_C1x6−80x6+160x3−80)23−63_C1x441_C1(−1+4−5x6−10x3+5_C1x6−80x6+160x3−80)(_C1x6−80x6+160x3−80)23))−1}

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