I need some help solving the differential equation y ‴ = x + y y ( 1 ) = 3 y ′ ( 1 ) = 2 y ″ ( 1 ) = 1and h=0.5 with Euler's methodI don't know how to rewrite the equation to a system of equations of the first order..

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I need some help solving the differential equation      y    ‴    =  x  +  y    y  (  1  )  =  3        y    ′    (  1  )  =  2        y    ″    (  1  )  =  1and h=0.5 with Euler&#039;s methodI don&#039;t know how to rewrite the equation to a system of equations of the first order..

Farbwolkenw · Accepted Answer

Here is how you linearize the system, we are given:      y    ‴    (  x  )  =  x  +  y  ,  y  (  1  )  =  3  ,      y    ′    (  1  )  =  2  ,      y    ″    (  1  )  =  1We can proceed as follows:      x    1    =  y    ⟹        x    1    ′    =      y    ′    =      x    2        x    2    =      y    ′      ⟹        x    2    ′    =      y    ″    =      x    3        x    3    =      y    ″      ⟹        x    3    ′    =      y    ‴    =  x  +  y  =  x  +      x    1  So, our new system is:                              x          1          ′                                    =                  x          2                                              x          2          ′                                    =                  x          3                                              x          3          ′                                    =        x        +                  x          1                    Note, the given initial conditions, similarly follow as:  y  (  1  )  =  3    ⟹        x    1    (  1  )  =  3      y    ′    (  1  )  =  2    ⟹        x    2    (  1  )  =  2      y    ″    (  1  )  =  1    ⟹        x    3    (  1  )  =  1Now, apply Euler&#039;s method to this system using   h  =  0.5.

I need some help solving the differential equation y′′′=x+y y(1)=3 y′(1)=2 y′′(1)=1 and h=0.5 with Euler's method

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