I have this differential equation y ′ = y ( sin ⁡ t ) t , y ( 0 ) = 2, and h = 1 4 . The first set of values, the inital, are (0,2). For the next iteration would it be y 1 = 2 + ( 1 4 ) ( 2 ⋅ sin ⁡ ( 0 ) 0 ) ? I know you can't divide by zero, so what would should I do in this case?

Question

I have this differential equation       y    ′    =            y      (      sin      ⁡      t      )        t  ,   y  (  0  )  =  2, and   h  =      1    4  . The first set of values, the inital, are (0,2). For the next iteration would it be       y    1    =  2  +  (      1    4    )      (                  2        ⋅        sin        ⁡        (        0        )            0        )  ? I know you can&#039;t divide by zero, so what would should I do in this case?

Audrey Russell · Accepted Answer

Use the fact that      lim          x      →      0                  sin      ⁡      (      x      )        x    =  1.

I have this differential equation y′=y(sint)/t, y(0)=2, and h=1/4.

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