## Differential Equations.

Limits, differentiation, related rates, integration, trig integrals, etc.
sepoto
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Joined: Thu Sep 19, 2013 3:38 am
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### Differential Equations.

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) $(\frac{d}{dx}+x)y=0$
--------------
b) $(\frac{dy}{dx}+xy)=0$

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:

$(1+x)y=0$

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

Thanks for any responses...

nona.m.nona
Posts: 288
Joined: Sun Dec 14, 2008 11:07 pm
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### Re: Differential Equations.

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) $(\frac{d}{dx}+x)y=0$
--------------
b) $(\frac{dy}{dx}+xy)=0$

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:

$(1+x)y=0$

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".