How do you work out if Euler's method overestimates the actual solution, for the ODE: d y d x = 24 tan ⁡ ( π x )With steps of 0.25 from 1 ≤ x ≤ 2?

Question

How do you work out if Euler&#039;s method overestimates the actual solution, for the ODE:            d      y              d      x        =  24  tan  ⁡  (  π  x  )With steps of 0.25 from   1  ≤  x  ≤  2?

Josie123 · Accepted Answer

d  y  =  24  tan  ⁡  (      π    x    )  d  x  ⇔  y  (  x  )  =  ∫  24  tan  ⁡  (      π    x    )  d  x  ⇔      24    π    ∫  tan  ⁡  (  u  )  d  u  =      24    π    ∫            s      i      n      (      u      )              c      o      s      (      u      )       Let   s  =  cos  ⁡  (  u  ) then   d  s  =  −  sin  ⁡  (  u  )  d  u so you get :  −      24    π    ∫      1    s    d  s  =  −      24    π    ln  ⁡  (  s  )  +  cSubstitute   s back in and you get :  −      24    π    ln  ⁡  (  s  )  +  c  =  −      24    π    ln  ⁡  (  c  o  s  (      π    x  )  )  +  cNow you can evaluate anything you want.

How do you work out if Euler's method overestimates the actual solution, for the ODE:

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