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# Differential Equation... I think watch

1. I need help with this question. It's from the OCR C4 specimen paper

For the curve 2x² + xy + y² = 14 find dy/dx in terms of x and y

Any help much appreciated

Chris
2. (Original post by needmathshelp)
I need help with this question. It's from the OCR C4 specimen paper

For the curve 2x² + xy + y² = 14 find dy/dx in terms of x and y

Any help much appreciated

Chris
This is implicit differentiation - which gives

4x + y + xy' + 2yy' = 0

Solving for y'

y' = (-4x-y)/(x+2y)
3. (Original post by needmathshelp)
I need help with this question. It's from the OCR C4 specimen paper

For the curve 2x² + xy + y² = 14 find dy/dx in terms of x and y

Any help much appreciated

Chris
[4x]+[x(dy/dx)+y]+[2y(dy/dx)]=0
4x+x(dy/dx)+y+2y(dy/dx)=0
(dy/dx)(x+2y)+4x+y=0
(dy/dx)(x+2y)=-(4x+y)
(dy/dx)=-(4x+y)/(x+2y)
4. sorted. We differentiate implicitly with respect to x.

We must differentiate xy as a product because y is a function of x.

2x² + xy + y² = 14

4x + x(dy/dx) + y +2y(dy/dx) = 0

And then rearrange...

If you don't know why it comes out as it does then ask again.
5. Thanks

It's all clear now

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