In Problems 1–4, use Euler's method to solve the first-order system subject to the specified initial condition. Use the given step size Δt and calculate the first three approximations (x_1, y₁), (x_2, y₂), and (x_3, y₃). Then repeat your calculations for Δt/2. Compare your approximations with the values of the given analytical solution.

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dx dt dy dt x (0) = 0, y (0) = 2. At 4 x (t)=-e-2 +3e1 - 2e', y(t) = e-1 + e1 = x + 3y = x - y +2e