I tried to do euler's method with this problem: d w d t = ( 3 − w ) ( w + 1 ) , w ( 0 ) = 0 , and t ∈ [ 0 , 5 ] . Δ t = 0.5.But am getting weird results like for y 2 = 5.25, y 3 = − 15.84375; but checked against the book but this is not correct. Can you please work out some iterations? y 2 = 1.5 + ( 3 − 1.5 ) ( 1.5 + 1 ) ( 1 ) = 5.25, for example

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I tried to do euler&#039;s method with this problem:            d      w              d      t        =  (  3  −  w  )  (  w  +  1  )  ,    w  (  0  )  =  0  ,    and   t  ∈  [  0  ,  5  ]  .    Δ  t  =  0.5.But am getting weird results like for       y    2    =  5.25,       y    3    =  −  15.84375; but checked against the book but this is not correct. Can you please work out some iterations?      y    2    =  1.5  +  (  3  −  1.5  )  (  1.5  +  1  )  (  1  )  =  5.25, for example

Marlee Norman · Accepted Answer

Euler&#039;s method in this case is       y          k      +      1        =      y    k    +  Δ  t  ⋅  (  3  −      y    k    )  (      y    k    +  1  ),       y    0    =  0. This gives       y    2    =  3.375 and       y    3    =  2.555. Note that   Δ  t  =  0.5.

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