Notation of differential equationsI have just started a course on differential equations, and unfortunetely enough for me, we immediately used notation foreign for me, for example: x 2 ( d 2 y d x 2 ) 2 = sin ⁡ ( x ) and y × d 2 y d x 2 = sin ⁡ ( x )were used as examples of non-linear ordinary differential equations. My questions are- Is d y d x equal to y′? Also, what then is d 2 y d x 2 ?I have looked up the formal mathematical definition but it somewhat confuses me,- Why on earth is this notation used, instead of just using ′ or ′′? It seems to me much more confusing and unnecessarily messy.

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Notation of differential equationsI have just started a course on differential equations, and unfortunetely enough for me, we immediately used notation foreign for me, for example:      x    2              (                                                  d              2                        y                                d                          x              2                                          )        2    =  sin  ⁡  (  x  )         and        y  ×                              d          2                y                    d                  x          2                      =  sin  ⁡  (  x  )were used as examples of non-linear ordinary differential equations. My questions are- Is                     d        y                    d        x             equal to y′? Also, what then is                               d          2                y                    d                  x          2                        ?I have looked up the formal mathematical definition but it somewhat confuses me,- Why on earth is this notation used, instead of just using ′ or ′′? It seems to me much more confusing and unnecessarily messy.

Brooklyn Mcintyre · Accepted Answer

Step 1Yes, your interpretation is correct:            d      y              d      x        =      y    ′       and likewise,                        d        2            y              d              x        2              =      y    ″  Step 2It&#039;s often simpler to use y′, I agree. But there are contexts, for example in implicit differentiation, or when x and y are defined in terms of a parameter, like t, in which using             d      y              d      x      , e.g., makes explicit that we want to differentiate y with respect to x. There are other advantages, but when no confusion or ambiguity results from using y′ to denote dydx, by all means, use it

Notation of differential equations. I have just started a course on differential equations, and unfortunetely enough for me, we immediately used notation foreign for me, for example: x^2 ((d^2y)/(dx^2))=sin(x) and y times (d^2y)/(dx^2)=sin(x)

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