Why aren't exact differential equations considered PDE?Exact differential equations come from finding the total differential from some multivariable function.In the exact differential equation M d x + N d y = 0M and N are considered to be partial derivatives of some potential function... So why aren't exact differential equations considered PDEs? After all, you're finding the potential function given it's partial derivatives...

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Why aren&#039;t exact differential equations considered PDE?Exact differential equations come from finding the total differential from some multivariable function.In the exact differential equation   M      d    x  +  N      d    y  =  0M and N are considered to be partial derivatives of some potential function... So why aren&#039;t exact differential equations considered PDEs? After all, you&#039;re finding the potential function given it&#039;s partial derivatives...

Monserrat Ellison · Accepted Answer

Step 1Because the partial differentials part is just a method of solving them, it&#039;s in the intermediate steps of a solution, not in the DE itself from the start. A bad example(can&#039;t think of a better one right now) would be considering   x  −  2  =  0 a second degree polynomial because you can introduce parameters and make it       x    2    =  4  ,  x  &amp;gt;  0.Step 2Also, consider being able to solve a D.E. by transforming it into exact equation by multiplying it with an integrating factor or by using another method that has nothing to do with partial derivatives. Why would you call that a PDE?A more specialized example would be      y    ′    =  y    ⟺        y    ′    −  y  =  0                            ⟺                            ⋅                  e                      −            x                                          y      ′              e      x        −      y          e      x        =  0

Why aren't exact differential equations considered PDE? In the exact differential equation Mdx+Ndy=0

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