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# 1st order differential substitution watch

1. Hi,
If the substitution is z=y^-2 and want to replace dy/dx by the chain rule:

dy/dx = dy/dz * dz/dx

y=z^-1/2
dy/dz = -1/2z^-3/2

so dy/dx= -1/2z^-3/2 *dz/dx

But... if z=y^-2

and diff each term wrt x:

dz/dx = -2y^-3 *dy/dx

so dy/dx = dz/dx * y^3/-2

Then subbing in for y and rearraning produces same answer..
Is both methods correct?
2. (Original post by 111davey1)
...
It's clearer if you just substitute in for

so yes both methods are correct and should give the same answer.

If then subbing in for you get

If

Now the only way where is if

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Updated: February 12, 2017
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