QCEVault

Differential equations — Question 106

Original QCE Vault practice · 6 marks

Q106 · Practice questionComplex unfamiliar6 marks

QUESTION 106 (6 marks)

A curve satisfies dydx=x1+y2,y(0)=0.\frac{dy}{dx}=\frac{x}{1+y^2},\qquad y(0)=0.
a)
Show that its solution can be written implicitly as y+y33=x22.y+\frac{y^3}{3}=\frac{x^2}{2}.
[3 marks]
b)
Use technology to determine yy when x=2x=2, to four decimal places.
[2 marks]
c)
Determine the gradient at that point, to four decimal places.
[1 mark]
Question linkSyllabus coverage

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