In Problems 14, use Euler's method to solve the first-order system subject to the specified initial condition. Use the given step size t and calculate

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.

dx dt dy dt x (0) = 2, y(0) = -1, At = x(t) = 3e1e2t, y(t) = e3t3te1 - 2e1 -tet 3x + e = -x + 3y +te1