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AQA FP3 Past Paper question

I just don't get question 3 in the paper here

http://filestore.aqa.org.uk/subjects/AQA-MFP3-W-QP-JAN06.PDF

I can do part a) and I've done the implicit differentiation but why is C/(x^2 -1) a solution. The mark scheme just says implies but I don't know why.

Mark scheme
http://filestore.aqa.org.uk/subjects/AQA-MFP3-W-MS-JAN06.PDF
Original post by maggiehodgson
I just don't get question 3 in the paper here

http://filestore.aqa.org.uk/subjects/AQA-MFP3-W-QP-JAN06.PDF

I can do part a) and I've done the implicit differentiation but why is C/(x^2 -1) a solution. The mark scheme just says implies but I don't know why.

Mark scheme
http://filestore.aqa.org.uk/subjects/AQA-MFP3-W-MS-JAN06.PDF


y=cx2−1y=\dfrac{c}{x^2-1} is a solution of dxdy+2xyx2−1=0\dfrac{dx}{dy}+\dfrac{2xy}{x^2-1}=0 because it satisfies the differential equation.

From your implicit differentiation you probably had 2xy+(x2−1)dydx=02xy+(x^2-1)\dfrac{dy}{dx}=0. Rearranging you obtain dydx=−2xyx2−1\dfrac{dy}{dx}=- \dfrac{2xy}{x^2-1}
Original post by BuryMathsTutor
y=cx2−1y=\dfrac{c}{x^2-1} is a solution of dxdy+2xyx2−1=0\dfrac{dx}{dy}+\dfrac{2xy}{x^2-1}=0 because it satisfies the differential equation.

From your implicit differentiation you probably had 2xy+(x2−1)dydx=02xy+(x^2-1)\dfrac{dy}{dx}=0. Rearranging you obtain dydx=−2xyx2−1\dfrac{dy}{dx}=- \dfrac{2xy}{x^2-1}



Thanks. Easy now I've been shown!

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