Question

Solve the following sets of recurrence relations and initial conditions:

S(k)−2S(k−1)+S(k−2)=2, S(0)=25, S(1)=16

The answer is: S(k)=k^2−10k+25

Please help me understand the solution. I get how to get the homogenous solution, I would get Sh(k) = a + bk

But I get stuck on the particular solution. Thanks

Answer #1

Solve the following recurrence relation, subject to the basis.
S(1) = 2 S(n) =2S(n/2) + 2n

Solve the following recurrence relation, subject to the
basis.
S(1) = 2
S(n) =2S(n/2) + 2n

Solve the recurrence relation an =
8an−1 −
16an−2 (n ≥ 2) with the
initial conditions a0 = 3 and a1 = 14. Show all your work.

solve the non-homogenous recurrence relation for
an =
2an-1+an-2-2an-3+8.3n-3 where
a0 = 2, a1 = 6 ve
a2=13
Find characteric equation by plugging
in an = rn
try to solve general solution and solve nonhomogeneous
particular solution
and find total final answer please..
My book anwer is
A(1)n+B(-1)n+C(2)n+k3n
, A=1/2, B=-1/2, C=1 ve k=1.
can you give me more explain about this please..?

Find the solution to the following lhcc recurrence:
??=−2??−1+24??−2 for ?≥2 with initial conditions a0=1,a1=4.
The solution is of the form: a?=?1(?1)^? + ?2(?2)^?
For suitable constants ?1,?2,?1,?2with ?1≤?2. Find these
constants.
r1=
r2=
a1=
a2=

Solve the separable equation 3xy^2 dy/dx = x^2 + 1 given y(0)
=5
I am getting a general solution of cubed root
x2/2+ln|x|+3c1 when I enter the initial
conditions y(0)=5 the equation is undefined. How do deal with this?
What would the final answer be?
Thanks

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