OCR A-level Mathematics A · H240

Differential equations

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QUESTION PAPER

Mathematics · A levelPure mathematics · H240/01

Torus Maths original · OCR style

For x≥0, a differentiable function y with $0<y<1$ satisfies $dy/dx=4xy^2(1-y)/(1+2x^2)$ and y(0)=1/2.

(a)

Find an implicit equation relating x and y.

[5]

(b)

Find the positive x-coordinate at which y=2/3, giving an exact answer.

[2]

(c)

Explain why the implicit equation gives exactly one value of y in (0,1) for each finite x≥0.

[2]

Question reference: ocr-a-level-pure-reviewed-33-01Report a question →

Answer booklet

Question 1 · Show your working

(a)

Answer booklet · Question 1(a)

(b)

Answer booklet · Question 1(b)

(c)

Answer booklet · Question 1(c)

Need a nudge?Three small hints · no answer revealed