Can these equations be considered as differential equations?Consider a differential equation with a term containing y ( x 0 ), for example y ″ − 2 y ′ + y = y ( x 0 ) x 0 ∈ R is a constant. My question is, does such equations fall under the category of differential equations? I have never studied any equation with such a term. If its a differential equation, then y ( x 0 ) can be considered a constant coefficient?

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Can these equations be considered as differential equations?Consider a differential equation with a term containing   y  (      x    0    ), for example      y    ″    −  2      y    ′    +  y  =  y  (      x    0    )      x    0    ∈      R   is a constant. My question is, does such equations fall under the category of differential equations? I have never studied any equation with such a term. If its a differential equation, then   y  (      x    0    ) can be considered a constant coefficient?

Leon Webster · Accepted Answer

Step 1Although the term   y  (      x    0    ) depends on the solution y it is still a constant as it doesn&#039;t depend on x.Let&#039;s try to solve your equation       y    ″    −  2      y    ′    +  y  =  C  ,, where   C  =  y  (      x    0    )  .. One solution is   y  (  x  )  =  C  . The solutions of the homogeneous equation are   y  (  x  )  =  (  A  x  +  B  )      e    x    .. Therefore the general solutions are  y  (  x  )  =  (  A  x  +  B  )      e    x    +  C  .Step 2To get   y  (      x    0    )  =  C we must have   A  =  B  =  0.. Thus there is only the constant solution  y  (  x  )  =  C  =  y  (      x    0    )  .

Can these equations be considered as differential equations? Consider a differential equation with a term containing y(x_0), for example y′′-2y′+y=y(x_0) x_0 in R is a constant.

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