My end goal is to solve for [itex]G(m)[/itex] in terms of the other functions, but first I have to solve the DE :(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\frac{d}{dm}[F(m) G(m)] = (\frac{d}{dm}F(m)) D(m)[/itex].

What I've done is to say (using integration by parts)

[itex]F(m) G(m) = F(m)D(m) - \int F(m) (\frac{d}{dm}D(m)) dm[/itex].

This is one method I tried. Another approach would be a separation of variables, which I tried as...

[itex]\frac{d}{dm}[F(m) G(m)] = \frac{dF}{dm} G + F \frac{dG}{dm} = \frac{dF}{dm} D [/itex]

which leads to...

[itex] \ln |F| = \int \frac{dG}{D - G} dm [/itex] and I believe that the RHS cannot be evaluated without specifying functions [itex]D[/itex] and [itex]G[/itex] (if the RHS can be evaluated without specification - please let me know...and please show me the way).

Help on understanding the correct method would be extremely appreciated.

Thanks in advance.

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# Solving DE- which approach and more importantly - why

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