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2.1745   ODE No. 1745

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

2(y(x)−a)y″(x)+y′(x)2+1=0 ✓ Mathematica : cpu = 0.298866 (sec), leaf count = 204

{{y(x)→InverseFunction[−2(12a−#1e2c1−2(a−#1)−e2c1tan−1⁡(2a−#1e2c1−2(a−#1))22)&][c2+x]},{y(x)→InverseFunction[2(12a−#1e2c1−2(a−#1)−e2c1tan−1⁡(2a−#1e2c1−2(a−#1))22)&][c2+x]}}

✓ Maple : cpu = 0.622 (sec), leaf count = 293

{−−(y(x))2+(2a+_C1)y(x)−a(_C1+a)+arctan⁡(1(y(x)−a−_C12)1−(y(x))2+(2a+_C1)y(x)−a(_C1+a))a+_C12arctan⁡(1(y(x)−a−_C12)1−(y(x))2+(2a+_C1)y(x)−a(_C1+a))−aarctan⁡(1(y(x)−a−_C12)1−(y(x))2+(2a+_C1)y(x)+a(−_C1−a))−x−_C2=0,−(y(x))2+(2a+_C1)y(x)−a(_C1+a)−arctan⁡(1(y(x)−a−_C12)1−(y(x))2+(2a+_C1)y(x)−a(_C1+a))a−_C12arctan⁡(1(y(x)−a−_C12)1−(y(x))2+(2a+_C1)y(x)−a(_C1+a))+aarctan⁡(1(y(x)−a−_C12)1−(y(x))2+(2a+_C1)y(x)+a(−_C1−a))−x−_C2=0}

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