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2.585   ODE No. 585

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

y′(x)=y(x)F(log⁡(log⁡(y(x)))−log⁡(x)) ✓ Mathematica : cpu = 120.541 (sec), leaf count = 202

Solve[∫1y(x)(1K[2](xF(log⁡(log⁡(K[2]))−log⁡(x))−log⁡(K[2]))−∫1x(F(log⁡(log⁡(K[2]))−log⁡(K[1]))(K[1]F′(log⁡(log⁡(K[2]))−log⁡(K[1]))K[2]log⁡(K[2])−1K[2])(K[1]F(log⁡(log⁡(K[2]))−log⁡(K[1]))−log⁡(K[2]))2−F′(log⁡(log⁡(K[2]))−log⁡(K[1]))K[2]log⁡(K[2])(K[1]F(log⁡(log⁡(K[2]))−log⁡(K[1]))−log⁡(K[2])))dK[1])dK[2]+∫1x−F(log⁡(log⁡(y(x)))−log⁡(K[1]))K[1]F(log⁡(log⁡(y(x)))−log⁡(K[1]))−log⁡(y(x))dK[1]=c1,y(x)]

✓ Maple : cpu = 0.485 (sec), leaf count = 168

{∫_bxF(ln⁡(ln⁡(y(x)))−ln⁡(_a))_aF(ln⁡(ln⁡(y(x)))−ln⁡(_a))−ln⁡(y(x))d_a+∫y(x)−1_f(xF(ln⁡(ln⁡(_f))−ln⁡(x))−ln⁡(_f))−∫_bx−F(ln⁡(ln⁡(_f))−ln⁡(_a))(_aF(ln⁡(ln⁡(_f))−ln⁡(_a))−ln⁡(_f))2(_aD(F)(ln⁡(ln⁡(_f))−ln⁡(_a))_fln⁡(_f)−_f−1)+D(F)(ln⁡(ln⁡(_f))−ln⁡(_a))(_aF(ln⁡(ln⁡(_f))−ln⁡(_a))−ln⁡(_f))_fln⁡(_f)d_ad_f+_C1=0}

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