# Thread: Express as a differential equation in terms of x, y and t

1. ## Express as a differential equation in terms of x, y and t

Given that two quantities x and y, both vary with time t. express the following statesments as differential equations involving x, y and t.

The rate of change of y with respect to t is inversely proportional to x.

$\displaystyle \frac{dy}{dt}=\frac{k}{x}$

How do I continue?

2. ## Re: Express as a differential equation in terms of x, y and t

I believe you are done.
You expressed the statement as a DE.

3. ## Re: Express as a differential equation in terms of x, y and t

Originally Posted by Punch
Given that two quantities x and y, both vary with time t. express the following statesments as differential equations involving x, y and t.

The rate of change of y with respect to t is inversely proportional to x.

$\displaystyle \frac{dy}{dt}=\frac{k}{x}$

How do I continue?
The DE is 'separable variables' and can be written as...

$\displaystyle x(t)\ dy = k\ dt$ (1)

If x(t) is known, then the solution is obtained in standard way integrating both terms of (1). If it isn't You need another DE to find x(t) and y(t)...

Marry Christmas from Serbia

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