Let be the solution to the differential equation with initial condition

MATHEMATICS · Numerical · AP · Calculus BC · Differential Equations · Differential Equations

Problem

Let y=f(x)y=f(x) be the solution to the differential equation dydx=x−y\frac{dy}{dx}=x-y with initial condition f(1)=3f(1)=3. What is the approximation for f(2)f(2) obtained by using Euler's method with two steps of equal length starting at x=1x=1?

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