MediumCalculusca-175

Difference Equation Solve

Problem

Solve the first-order linear recurrence y[n] = a*y[n-1] + b with y[0] = y0 in closed form.

For a != 1 the solution is y[n] = a^n * y0 + b * (1 - a^n) / (1 - a); for a = 1 it is y[n] = y0 + n*b. Given a, b, y0, and n >= 0, return y[n].

Hint

The fixed point b/(1-a) plus a transient a^n controls the solution.

case 1

in: [0.5,1,0,3]

expected: 1.75

case 2

in: [1,2,5,4]

expected: 13

case 3

in: [2,0,3,5]

expected: 96

case 4

in: [0.5,2,1,10]

expected: 3.9970703125

Starter codePython

def difference_equation(a, b, y0, n):
    # Your code here
    pass

4 test cases · run your code against them in the editor