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3.562   ODE No. 562

a(ddxy(x))3+13+bxddxy(x)−y(x)=0

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

Mathematica: cpu = 264.371071 (sec), leaf count = 119 Solve[{x=a(b−1)K$14864203(K$1486420−bK$1486420)b1−b+1b−12F1(23,2−3b3−3b;5−6b3−3b;−K$14864203)3b−2+c1(K$1486420−bK$1486420)b1−b,y(x)=aK$14864203+13+bK$1486420x},{y(x),K$1486420}]

Maple: cpu = 0.094 (sec), leaf count = 3961 {x−(12b3x3+2a3(2b2x2y(x)−4b6x6−8a3b3x3−4b3x3(y(x))3+4b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6b3x3−4a6+4(y(x))3a3+4a3b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))63−4(y(x))2a2bx+a(−4b6x6−8a3b3x3−4b3x3(y(x))3+4b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6b3x3−4a6+4(y(x))3a3+4a3b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6)23)1−4b6x6−8a3b3x3−4b3x3(y(x))3+4b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6b3x3−4a6+4(y(x))3a3+4a3b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))63)−bb−1(∫12b3x3+2a3(2b2x2y(x)−4b6x6−8a3b3x3−4b3x3(y(x))3+4b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6b3x3−4a6+4(y(x))3a3+4a3b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))63−4(y(x))2a2bx+a(−4b6x6−8a3b3x3−4b3x3(y(x))3+4b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6b3x3−4a6+4(y(x))3a3+4a3b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6)23)1−4b6x6−8a3b3x3−4b3x3(y(x))3+4b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6b3x3−4a6+4(y(x))3a3+4a3b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))63−ab−1_a1+bb−1(_a3+1)−23d_a+_C1)=0,x−(−14b3x3+4a3(4i3a2bx(y(x))2−4b2x2y(x)−4b6x6−8a3b3x3−4b3x3(y(x))3+4b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6b3x3−4a6+4(y(x))3a3+4a3b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))63−4(y(x))2a2bx+i3(−4b6x6−8a3b3x3−4b3x3(y(x))3+4b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6b3x3−4a6+4(y(x))3a3+4a3b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6)23a+a(−4b6x6−8a3b3x3−4b3x3(y(x))3+4b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6b3x3−4a6+4(y(x))3a3+4a3b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6)23)1−4b6x6−8a3b3x3−4b3x3(y(x))3+4b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6b3x3−4a6+4(y(x))3a3+4a3b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))63)−bb−1(∫−14b3x3+4a3(4i3a2bx(y(x))2−4b2x2y(x)−4b6x6−8a3b3x3−4b3x3(y(x))3+4b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6b3x3−4a6+4(y(x))3a3+4a3b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))63−4(y(x))2a2bx+i3(−4b6x6−8a3b3x3−4b3x3(y(x))3+4b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6b3x3−4a6+4(y(x))3a3+4a3b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6)23a+a(−4b6x6−8a3b3x3−4b3x3(y(x))3+4b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6b3x3−4a6+4(y(x))3a3+4a3b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6)23)1−4b6x6−8a3b3x3−4b3x3(y(x))3+4b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6b3x3−4a6+4(y(x))3a3+4a3b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))63−ab−1_a1+bb−1(_a3+1)−23d_a+_C1)=0,x−(14b3x3+4a3(4i3a2bx(y(x))2+4b2x2y(x)−4b6x6−8a3b3x3−4b3x3(y(x))3+4b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6b3x3−4a6+4(y(x))3a3+4a3b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))63+4(y(x))2a2bx+i3(−4b6x6−8a3b3x3−4b3x3(y(x))3+4b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6b3x3−4a6+4(y(x))3a3+4a3b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6)23a−a(−4b6x6−8a3b3x3−4b3x3(y(x))3+4b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6b3x3−4a6+4(y(x))3a3+4a3b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6)23)1−4b6x6−8a3b3x3−4b3x3(y(x))3+4b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6b3x3−4a6+4(y(x))3a3+4a3b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))63)−bb−1(∫14b3x3+4a3(4i3a2bx(y(x))2+4b2x2y(x)−4b6x6−8a3b3x3−4b3x3(y(x))3+4b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6b3x3−4a6+4(y(x))3a3+4a3b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))63+4(y(x))2a2bx+i3(−4b6x6−8a3b3x3−4b3x3(y(x))3+4b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6b3x3−4a6+4(y(x))3a3+4a3b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6)23a−a(−4b6x6−8a3b3x3−4b3x3(y(x))3+4b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6b3x3−4a6+4(y(x))3a3+4a3b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6)23)1−4b6x6−8a3b3x3−4b3x3(y(x))3+4b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))6b3x3−4a6+4(y(x))3a3+4a3b6x6+2a3b3x3+2b3x3(y(x))3+a6−2(y(x))3a3+(y(x))63−ab−1_a1+bb−1(_a3+1)−23d_a+_C1)=0}

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