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AP Calculus BC/Unit 7: Differential Equations
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Euler's Method Two Step Approximation

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Let y=f(x)y = f(x) be the solution to the differential equation dydx=x−y\displaystyle \frac{dy}{dx} = x - y with the initial condition f(2)=8f(2) = 8. Using Euler’s method with two equal steps starting at x=2x = 2, what is the approximation of f(3)f(3)?

A

52\displaystyle \frac{5}{2}

B

154\displaystyle \frac{15}{4}

C

22

D

614\displaystyle \frac{61}{4}

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