What manipulation has been done here?

Chet T16

In going for the top to the bottom i can't figure out whats been done and i'll bet its something embarrassingly simple :rolleyes:

VW 1

Chet T16 wrote: »

In going for the top to the bottom i can't figure out whats been done and i'll bet its something embarrassingly simple :rolleyes:

bring the x across the = sign and it becomes 1 over x
3-y back across the = sign and it beomes 1 over 3-y.
which leaves you with 1/3-y dy/dx= 1/x

gerardduff

Chet T16 wrote: »

Do you want to actually solve this equation? I'm guessing you will so here's a clue to help you along....

First, I thought you had used latex there. :pac:

You might like to know how that image was created so I'll do this in latex and you can see how it works, just look at it with the quote button

To solve, rearrange the equation as,

[latex]\displaystyle x\frac{dy}{dx} + y=3 [/latex]

Here's the clue

Now the left hand side is the result of applying the product rule to

[latex]xy[/latex]

Now I feel like Rolf Harris ('Do you know what it is yet? said in Aussie accent). Hope I haven't ruined it for you. Please try to do this before viewing the spoiler, which you do by highlighting it (as if to copy it).

You can write the equation as...

[latex]\frac{d}{dx}xy=3[/latex]

MathsManiac

Chet T16 wrote: »

In going for the top to the bottom i can't figure out whats been done and i'll bet its something embarrassingly simple :rolleyes:

Both sides have been divided by 3-y, and both sides have been divided by x.

It's useful to remember that all such manipulations involve doing the same thing to both sides of the equation.