section 2

Question 1

how to solve a 3 step DE

Answer 1

set xn= A. (lambda)^n
divide through by A and (lambda)^n
solve to find lambda
then the GS is
xn= A (lambda1)^n + B(lambda2)^n where A and B are constants
to find PS, set n=0 and n=1 if thats what given and use simultaneous equations

Question 2

how to solve the Fibonacci equation

Answer 2

set xn= A. (lambda)^n
divide by A and (lambda)^n 
solve for lambda for a positive and negative 
GS is xn= A(lambda+)^n + B(lambda-)^n 
use simultaneous equations to find PS

Question 3

solving 3 step difference equations with repeated roots

Answer 3

GS is written as xn= A.(lambda)^n + n.B.(lambda)^n

Question 4

what is newtons law of cooling as an equation

Answer 4

differentiate theta w.r.t t (time) = -k( theta- a)

where temp= theta
ambient temp= a (background)
k= some positive constant

Question 5

liquid mixing equation

Answer 5

theta= (V1. theta1 +v2. theta 2) / (V1+ V2)

where V= volume
theta= temperature