For the systemwe claim that the curve Y(t) = (e2t, 3et) is a solution. Its initial positio...

For the system

we claim that the curve Y(t) = (e2t, 3et) is a solution. Its initial position is Y(0) = (1, 3).

(a) Check that Y(t) = (e2t, 3et) is a solution.

(b) Use Euler’s method with step size Δt = 0.5 to approximate this solution, and check how close the approximate solution is to the real solution when t = 2, t = 4, and t = 6.

(c) Use Euler’s method with step size Δt = 0.1 to approximate this solution, and check how close the approximate solution is to the real solution when t = 2, t = 4, and t = 6.

(d) Discuss how and why the Euler approximations differ from the solution.

[Use a computer or calculator to perform Euler’s method.]