Find the solution to the equation Ur+1= 4Ur + 3?
U1 = 6
Test your answer by finding the value of u4 in 2 different ways: by substitution in your solution and by repeated evaluation of the equation.
sorry about the equation problem
Test the answer by finding the value of in 2 different ways:
by substitution in your solution and by repeated evaluation of the equation.
by substitution I have found u2=27,u3=111 and u4=447
I'm wondering how to find these values by repeated evaluation of the equation?
Cheers
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I think you are trying to solve the difference equation
I think there is a typo and you are missing the +1
So to solve we do it in two parts:
First we solve the homogenous equation
we use the "guess"
Plugging this in gives
this gives
so the solution has the form
Since the right hand side is a constant we guess that the particular solution is also a constant
So the solution is
Now using the initial condition gives
So the solution is
Now if we plug in
we get