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

• Dec 17th 2011, 07:31 PM
Punch
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.

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

How do I continue?
• Dec 17th 2011, 09:09 PM
ILikeSerena
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.

• Dec 17th 2011, 11:04 PM
chisigma
Re: Express as a differential equation in terms of x, y and t
Quote:

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.

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

How do I continue?

The DE is 'separable variables' and can be written as...

$x(t)\ dy = k\ dt$ (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)...

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