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Year 12 Specialist (Unit 3 & 4) Rates of change and differential equations

Slope field for a differential equation.

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Questions
Question 1
16016

Given the differential equation \(\dfrac{{dy}}{{dx}} = y + \dfrac{x}{3}\) and given that the solution curve passes through point \((6,-1)\), then the gradient of the solution curve at this point is?

A.

\(1\)

B.

\(-1\)

C.

\(5\dfrac{2}{3}\)

D.

\(-5\dfrac{2}{3}\)

\(1\)

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