(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm trying to make sense of the steps for solving a linear differential equation and I'm stuck at the part where

[tex] \mu (x) \frac{\mathrm{d}y}{\mathrm{d}x} + \mu (x) P(x)y=\frac{\mathrm{d}}{\mathrm{d}x} [\mu (x)y] [/tex]

I guess I'm not sure what [itex] \frac{\mathrm{d}}{\mathrm{d}x} [/itex] even means. Doesn't it mean the derivative with respect to x?

Here's an example, perhaps that will help to clarify the trouble.

[tex] x^{-2} \frac{\mathrm{d}y}{\mathrm{d}x} - 2x^{-3}y [/tex] is supposedly equivalent to

[tex] \frac{\mathrm{d}}{\mathrm{d}x} (x^{-2}y) [/tex]

Now how does that equate?

2. Relevant equations

3. The attempt at a solution

The derivative of [tex] (x^{-2}y) [/tex] is [tex] - 2x^{-3}y [/tex].

So... why doesn't [tex] \frac{\mathrm{d}}{\mathrm{d}x} (x^{-2}y) = - 2x^{-3}y [/tex] ?

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# Homework Help: Solving linear differential equation

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