C4 differential equations, basic help

My writing with latex isn't very good so i apologise in advance.

I'm a little confused on why different methods have been used in the following equations. On the first one dy/dt had been rearranged so its dt/dy, and then integrated. However on the second one the variables have been separated.

Why can't I do dt/dv on the second one (like the first method), and how do I know that I need to separate the variables?

First equation:

Second equation:

Reply 1

Intriguing Alias

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Original post by newskills

My writing with latex isn't very good so i apologise in advance.

I'm a little confused on why different methods have been used in the following equations. On the first one dy/dt had been rearranged so its dt/dy, and then integrated. However on the second one the variables have been separated.

Why can't I do dt/dv on the second one (like the first method), and how do I know that I need to separate the variables?

First equation:

Second equation:

You're basically doing the same thing in both. In the end for the first question you actually did

\int dt = \int \dfrac{1}{5y} dy

. A quicker way to do that is 'separating the variables' as in the second question.

When you have differentials of the form f(xy) then you'll see why separating the variables in the way shown in the second question is the most desirable.

Reply 2

newskills

OP

Thanks, thats cleared things up :smile:

C4 differential equations, basic help

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