What is the Correct Solution for the Difference Equation yn+1=-0.9yn?

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SUMMARY

The correct solution for the difference equation yn+1 = -0.9yn is yn = (-0.9)ny0, which aligns with the derivation provided in the forum discussion. The textbook presents the solution as yn = (-1)n(0.9)ny0 to emphasize the sign alternation between even and odd terms. Both forms are mathematically equivalent, as demonstrated by substituting yn into the original equation to verify that -0.9yn = yn+1 holds true. This confirms that the derived solution satisfies the difference equation.

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Solve the difference equation yn+1=-0.9yn in terms of the initial value y0.

y1=-0.9y0
y2=-0.9y1=(-0.9)2y0
yn=(-0.9)ny0
Is this the answer? Because the answer in the textbook says yn=(-1)n(0.9)ny0. Please help.
 
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Your solution and the solution in your textbook are the same.
 
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(ab)^n= a^n b^n
 
The textbook wrote it that way to make it clear that even terms are positive and odd terms are negative.
 
And, as I pointed out in your previous thread, you are not finished until you have shown that your solution does satisfy the equation. If yn= (-0.9)ny0 then -0.9yn= -0.9((-0.9)ny0)= (-0.9)n+1y0= yn+1.
 

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