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8.128   ODE No. 1718

(d2dx2y(x))y(x)+a(ddxy(x))2+by(x)ddxy(x)+c(y(x))2+d(y(x))1−a=0

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

Mathematica: cpu = 1.508191 (sec), leaf count = 744 {{y(x)→(−adexp⁡(12x(−4ac+b2−4c+b)−x(b−4ac+b2−4c−4(a+1)c+b2)−4ac+b2−4c+b−2(a+1)cx−4ac+b2−4c+b)(a+1)c−dexp⁡(12x(−4ac+b2−4c+b)−x(b−4ac+b2−4c−4(a+1)c+b2)−4ac+b2−4c+b−2(a+1)cx−4ac+b2−4c+b)(a+1)c+abc1exp⁡(−x(b−4ac+b2−4c−4(a+1)c+b2)−4ac+b2−4c+b−2(a+1)cx−4ac+b2−4c+b)b−4ac+b2−4c−4ac+b2−4c+bc1exp⁡(−x(b−4ac+b2−4c−4(a+1)c+b2)−4ac+b2−4c+b−2(a+1)cx−4ac+b2−4c+b)b−4ac+b2−4c−4ac+b2−4c+ac1−4ac+b2−4cexp⁡(−x(b−4ac+b2−4c−4(a+1)c+b2)−4ac+b2−4c+b−2(a+1)cx−4ac+b2−4c+b)b−4ac+b2−4c−4ac+b2−4c+c1−4ac+b2−4cexp⁡(−x(b−4ac+b2−4c−4(a+1)c+b2)−4ac+b2−4c+b−2(a+1)cx−4ac+b2−4c+b)b−4ac+b2−4c−4ac+b2−4c+c2e−2(a+1)cx−4ac+b2−4c+b)1a+1}}

Maple: cpu = 0.187 (sec), leaf count = 158 {y(x)=1(c2(−4ac+b2−4c)(_C2ce−x2(−b+−4ac+b2−4c)a−ex2(b+−4ac+b2−4c)_C1ac+_C2ce−x2(−b+−4ac+b2−4c)−debx−4ac+b2−4c−ex2(b+−4ac+b2−4c)_C1c)−2)−12a+2(ebxa+1)−1}

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