About differential equations.1. While solving differential equations, is it okay to find an expression containing y and x (without y′) from which it's rather difficult to express y, for example, ln 2 ⁡ ( y ) y − x y = C ?2. Does it make sense to try to find x(y) in some problems where it's easier?

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About differential equations.1. While solving differential equations, is it okay to find an expression containing y and x (without y′) from which it&#039;s rather difficult to express y, for example,                    ln        2            ⁡      (      y      )        y    −      x    y    =  C  ?2. Does it make sense to try to find x(y) in some problems where it&#039;s easier?

gasskadeu7 · Accepted Answer

Step 11) Yes, it is typical to find the solution in a manner where y and x are implicitly defined.Step 22) Yes, in some cases it is easier to express   x  =  f  (  y  ) instead of   y  =  g  (  x  ).

tamola7f · Accepted Answer

Step 1For instance, in the case of a separable equation such as g(y)dy=f(x)dx, you are lucky if both members can be integrated analytically.Step 2Then you obtain a form like  G  (  y  )  =  F  (  x  )  +  cand you are even more lucky if G is invertible analytically. It can arise that G is not monotonic, and the solution must be split in several branches.

About differential equations. 1. While solving differential equations, is it okay to find an expression containing y and x (without y′) from which it's rather difficult to express y, for example, (ln^2(y))/(y)-x/y=C?

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