The problem I have is the initial value problem y ‴ = x + ywith y ( 1 ) = 3 , y ′ ( 1 ) = 2 , y ″ ( 1 ) = 1that should be solved with Eulers method using the step length, h = 1 2 .The iteration step for Eulers method is y n + 1 = y n + h f ( x n , y n ). So I should need a system of equations of my initial values I have. I started with substituting: U 1 = y , U 2 = y ′ , U 3 = y ″ and then U 1 ′ = U 2 , U 2 ′ = U 3 , U 3 ′ = x + U 1 And it's here I'm stuck, I don't understand how I should start iterate with the step-length from here, I have only encounteblack first-order problem with Eulers method so I would love if someone could point me in the right direction.

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The problem I have is the initial value problem      y    ‴    =  x  +  ywith  y  (  1  )  =  3  ,      y    ′    (  1  )  =  2  ,      y    ″    (  1  )  =  1that should be solved with Eulers method using the step length,   h  =      1    2  .The iteration step for Eulers method is       y          n      +      1        =      y    n    +  h  f  (      x    n    ,      y    n    ). So I should need a system of equations of my initial values I have. I started with substituting:      U    1    =  y  ,      U    2    =      y    ′    ,      U    3    =      y    ″  and then      U    1    ′    =      U    2    ,      U    2    ′    =      U    3    ,      U    3    ′    =  x  +      U    1  And it&#039;s here I&#039;m stuck, I don&#039;t understand how I should start iterate with the step-length from here, I have only encounteblack first-order problem with Eulers method so I would love if someone could point me in the right direction.

tangouwn · Accepted Answer

y    ‴    (  1  )  =  y  (  1  )  +  (  x  =  1  ) To get it going.  y  (  1  +  1  h  )  =  y  (  1  )  +      y    ′    (  1  )  h      y    ′    (  1  +  1  h  )  =      y    ′    (  1  )  +      y    ″    (  1  )  h      y    ″    (  1  +  1  h  )  =      y    ″    (  1  )  +      y    ‴    (  1  )      y    ‴    (  1  +  1  h  )  =  y  (  1  )  +  (  x  =  1  )repeat from step 2

June Mejia · Accepted Answer

Good

The problem I have is the initial value problem y′′′=x+y with y(1)=3,y′(1)=2,y′′(1)=1 that should be solved with Eulers method using the step length, h=1/2.

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