# Solving difference equation with its initial conditions

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Ben Le on 19 Feb 2017
Edited: Ben Le on 21 Feb 2017
Hi,
Consider a difference equation:
8*y[n] - 6*y[n-1] + 2*y[n-2] = 1
with initial conditions
y= 0 and y[-1]=2
How can I determine its plot y(n) in Matlab? Thank you in advance for your help!
##### 2 CommentsShowHide 1 older comment
Walter Roberson on 19 Feb 2017
I would call this a recurrence equation, not a difference equation.

Jan on 21 Feb 2017
Edited: Jan on 21 Feb 2017
Resort the terms:
8*y[n] - 6*y[n-1] + 2*y[n-2] = 1
y[n] = (1 + 6*y[n-1] - 2*y[n-2]) / 8
or in Matlab:
y(n) = (1 + 6*y(n-1) - 2*y(n-2)) / 8;
Now the indices cannot start at -1, because in Matlab indices are greater than 0. This can be done by a simple translation:
y = zeros(1, 100); % Pre-allocate
y(1:2) = [2, 0];
for k = 3:100
y(k) = (1 + 6*y(k-1) - 2*y(k-2)) / 8;
end
Now you get the y[i] by y(i+2).
Ben Le on 21 Feb 2017
Edited: Ben Le on 21 Feb 2017
Thank you so much, Jan!!!!

Sindhuja Parimalarangan on 21 Feb 2017
This link discusses solving recurrence equations using MATLAB. The discrete solution for "y" can be plotted using the stem function.

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