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# Differential Equations watch

1. So according to this differential equation

dy
dx
=
x2
y

- If f(x) = xsquared
g(y) = 1/y

why when integrating does

ydy = xsquared dx?

(ie- what happened to the 1/y?)

Thanks
2. (Original post by Kieran578)
So according to this differential equation

dy
dx
=
x2
y

- If f(x) = xsquared
g(y) = 1/y

why when integrating does

ydy = xsquared dx?

(ie- what happened to the 1/y?)

Thanks
You've got the equation:

Remember that, in essence, and are just small bits of and respectively. Thus, you can 'rearrange' the equation in a similar way to one you're used to:

- multiply through by y
- multiply through by dx

which gives you

Then you integrate that...etc. Hope that makes sense.
3. (Original post by james.h)
You've got the equation:

- multiply through by y
- multiply through by dx

which gives you

Then you integrate that...etc. Hope that makes sense.

Could you quickly demonstrate the multipying through part as i cant quite get my head around it (not why you do it, but how)
4. dy/dx = x^2/y

so multiply through by y => (ydy)/dx = (yx^2)/y

y/y on the right hand side cancels => (ydy)/dx = x^2

multiply through by dx => (dxydy)/dx = x^2 dx

dx/dx on the left hand side cancels => ydy = x^2 dx
5. (Original post by Shawshank)
dy/dx = x^2/y

so multiply through by y => (ydy)/dx = (yx^2)/y

y/y on the right hand side cancels => (ydy)/dx = x^2

multiply through by dx => (dxydy)/dx = x^2 dx

dx/dx on the left hand side cancels => ydy = x^2 dx

Thanks

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