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3.586   ODE No. 586

ddxy(x)=xx2+1F(y(x)x2+1)=0

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

Mathematica: cpu = 143.313198 (sec), leaf count = 972 Solve[∫1y(x)(−x2+1F(K[2]x2+1)−x2F(K[2]x2+1)2−F(K[2]x2+1)2+K[2]2−∫1x(K[1]K[1]2+1(2F(K[2]K[1]2+1)F′(K[2]K[1]2+1)K[1]2K[1]2+1−2K[2]+2F(K[2]K[1]2+1)F′(K[2]K[1]2+1)K[1]2+1)F(K[2]K[1]2+1)3K[2](K[1]2F(K[2]K[1]2+1)2+F(K[2]K[1]2+1)2−K[2]2)2+K[1]K[1]2+1F(K[2]K[1]2+1)3K[2]2(K[1]2F(K[2]K[1]2+1)2+F(K[2]K[1]2+1)2−K[2]2)−3K[1]F′(K[2]K[1]2+1)F(K[2]K[1]2+1)2K[2](K[1]2F(K[2]K[1]2+1)2+F(K[2]K[1]2+1)2−K[2]2)+K[1](2F(K[2]K[1]2+1)F′(K[2]K[1]2+1)K[1]2K[1]2+1−2K[2]+2F(K[2]K[1]2+1)F′(K[2]K[1]2+1)K[1]2+1)F(K[2]K[1]2+1)2(K[1]2F(K[2]K[1]2+1)2+F(K[2]K[1]2+1)2−K[2]2)2−2K[1]F′(K[2]K[1]2+1)F(K[2]K[1]2+1)K[1]2+1(K[1]2F(K[2]K[1]2+1)2+F(K[2]K[1]2+1)2−K[2]2)−K[1]F(K[2]K[1]2+1)K[1]2+1K[2]2+K[1]F′(K[2]K[1]2+1)(K[1]2+1)K[2])dK[1]−K[2]−x2F(K[2]x2+1)2−F(K[2]x2+1)2+K[2]2)dK[2]+∫1x(−K[1]K[1]2+1F(y(x)K[1]2+1)3y(x)(K[1]2F(y(x)K[1]2+1)2+F(y(x)K[1]2+1)2−y(x)2)−K[1]F(y(x)K[1]2+1)2K[1]2F(y(x)K[1]2+1)2+F(y(x)K[1]2+1)2−y(x)2+K[1]F(y(x)K[1]2+1)K[1]2+1y(x))dK[1]=c1,y(x)]

Maple: cpu = 0.203 (sec), leaf count = 39 {y(x)=RootOf(−ln⁡(x2+1)+2∫_Z(F(_a)−_a)−1d_a+2_C1)x2+1}

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