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3.432   ODE No. 432

(xddxy(x)+a)2−2ay(x)+x2=0

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

Mathematica: cpu = 1.713718 (sec), leaf count = 64 Solve[{y(x)=a2+2aK$1274426x+K$12744262x2+x22a,x=c1K$12744262+1−asinh−1⁡(K$1274426)K$12744262+1},{y(x),K$1274426}]

Maple: cpu = 7.551 (sec), leaf count = 615 {y(x)=−(RootOf((Arcsinh(_Z))2a2−_Z2x2−2Arcsinh(_Z)_C1a+_C12−x2))4x2−2(RootOf((Arcsinh(_Z))2a2−_Z2x2−2Arcsinh(_Z)_C1a+_C12−x2))2a−2a+2Arcsinh(RootOf((Arcsinh(_Z))2a2−_Z2x2−2Arcsinh(_Z)_C1a+_C12−x2))(RootOf((Arcsinh(_Z))2a2−_Z2x2−2Arcsinh(_Z)_C1a+_C12−x2))2+1RootOf((Arcsinh(_Z))2a2−_Z2x2−2Arcsinh(_Z)_C1a+_C12−x2)a2−2(RootOf((Arcsinh(_Z))2a2−_Z2x2−2Arcsinh(_Z)_C1a+_C12−x2))2a−2a−(RootOf((Arcsinh(_Z))2a2−_Z2x2−2Arcsinh(_Z)_C1a+_C12−x2))2a2−2(RootOf((Arcsinh(_Z))2a2−_Z2x2−2Arcsinh(_Z)_C1a+_C12−x2))2a−2a−2(RootOf((Arcsinh(_Z))2a2−_Z2x2−2Arcsinh(_Z)_C1a+_C12−x2))2x2−2(RootOf((Arcsinh(_Z))2a2−_Z2x2−2Arcsinh(_Z)_C1a+_C12−x2))2a−2a−2(RootOf((Arcsinh(_Z))2a2−_Z2x2−2Arcsinh(_Z)_C1a+_C12−x2))2+1_C1RootOf((Arcsinh(_Z))2a2−_Z2x2−2Arcsinh(_Z)_C1a+_C12−x2)a−2(RootOf((Arcsinh(_Z))2a2−_Z2x2−2Arcsinh(_Z)_C1a+_C12−x2))2a−2a−a2−2(RootOf((Arcsinh(_Z))2a2−_Z2x2−2Arcsinh(_Z)_C1a+_C12−x2))2a−2a−x2−2(RootOf((Arcsinh(_Z))2a2−_Z2x2−2Arcsinh(_Z)_C1a+_C12−x2))2a−2a}

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