I have equation: d y d t = − 0.04 y How would I find the expression for Euler's method? I know the general expression is: y n = y n − 1 + h ⋅ F ( t n − 1 , y n − 1 )but I am confused with what to use as x and y and how I could convert − 0.04 y into that form.Edit: increments of 1 second, y ( 0 ) = 3.

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I have equation:                                                        d                        y                                              d                        t                          =        −        0.04                  y                    How would I find the expression for Euler&#039;s method? I know the general expression is:      y    n    =      y          n      −      1        +  h  ⋅  F  (      t          n      −      1        ,      y          n      −      1        )but I am confused with what to use as x and y and how I could convert   −  0.04      y   into that form.Edit: increments of 1 second,   y  (  0  )  =  3.

Boatein · Accepted Answer

Let&#039;s consider the initial condition  y  (  0  )  =      y    0    .Then      y    ′    (  0  )  =  F  (  0  ,      y    0    )  =  −  0.04            y      0        .Then assuming a time step   Δ  t  =  h we can estimate  y  (  h  )  ≈      y    1    =  y  (  0  )  +      y    ′    (  0  )  ⋅  Δ  t  =      y    0    +      y    0    ′    ⋅  h    ⟹    F  (  h  ,      y    1    )  =  −  0.04            y      1        .Then  y  (  2  h  )  ≈      y    2    =      y    1    +  h  ⋅  F  (  h  ,      y    0    )    ⟹    F  (  2  h  ,      y    2    )  =  −  0.04            y      2      and so on.

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