Differential Equations.  TOPIC_SOLVED

Limits, differentiation, related rates, integration, trig integrals, etc.

Differential Equations.

Postby sepoto on Wed Dec 11, 2013 7:06 am

I am studying differential equations and I have a question about whats in my lecture notes. Here is a link to the lecture notes:

http://sdrv.ms/1gYECTo

a)
--------------
b)

In the first equation above a) I am trying to get a handle on what is meant by having "d/dx" and "x" on the same side of the equation. I know that the derivative of "x" is "1" by the power rule. So then could the first equation above a) not reduce to:



or is something different meant by the use of "d/dx"?

Thanks for any responses...
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Re: Differential Equations.  TOPIC_SOLVED

Postby nona.m.nona on Wed Dec 11, 2013 11:44 am

sepoto wrote:I am studying differential equations and I have a question about whats in my lecture notes. Here is a link to the lecture notes:

MIT OpenCourseWare 18.01 Single Variable Calculus Fall 2006

a)
--------------
b)

In the first equation above a) I am trying to get a handle on what is meant by having "d/dx" and "x" on the same side of the equation. I know that the derivative of "x" is "1" by the power rule. So then could the first equation above a) not reduce to:



or is something different meant by the use of "d/dx"?

The "d/dx" is meant to apply (after "multiplication") to the y being multiplied on the right. The "d/dx" is not operating on the x within the grouping symbols, because the expression is "d/dx + x" rather than "dx/dx".

For further information on this sort of manipulation of the infinitesimals, try "the differential" (a discussion) and "Teaching Differentials as Fractions".
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