Hello guys could anyone please help me with this problem for

Hello guys,

could anyone please help me with this problem for my Math modeling class. A pic of the problem is attached below (6.1).

NOTE: please explain why for each case.

Thanks in advance,

6.1. Consider the following equations and identity as 1. Consider the following equations and ident linear or nonlinear homogeneous or nonhomogenous which order llnear or nonlinear a) Tn-1 (b) xn+1 = Zn-1 + 2 (c) xn+1=sin(xn-1) 2

Solution

a)x_{n+1} has power 2 so equation is non linear

There is constant term =1. so non homogeneous

x_{n+1} depends on xn so first order

b)

All xi\'s has power 1 so linear equation

There is a constnat term 2 so non homogeneous

x_n+1 depends on x_{n-1} ie 2 terms below itself so 2nd order

c)

non linear as x_{n-1 is arguement of a non linear function

homogeneous as no constant terms

order is 2 as in part b.

d)

Linear as all xis has power 1

Non homogeneous due to the term n^2

order is 6 as x_{n+3} depends on x_{n-3} which 6 terms below