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

[Success]

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

y₁=-0.9y₀
y₂=-0.9y₁=(-0.9)²y₀
y_n=(-0.9)ⁿy₀
Is this the answer? Because the answer in the textbook says y_n=(-1)ⁿ(0.9)ⁿy₀. Please help.

 

[krome]

Your solution and the solution in your textbook are the same.

 

[HallsofIvy]

(ab)^n= a^n b^n

 

[jedishrfu]

The textbook wrote it that way to make it clear that even terms are positive and odd terms are negative.

 

[HallsofIvy]

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 y_n= (-0.9)ⁿy₀ then -0.9y_n= -0.9((-0.9)ⁿy₀)= (-0.9)ⁿ⁺¹y₀= y_n+1.