Answer:
a)
.
b)
c)

Step-by-step explanation:
a) The given differential equation is:
.
The characteristic equation is: 
This implies that: 
The auxiliary solution to this second order homogeneous differential equation is: 
Therefore any equation of the
where A and B are constants is a solution
.
.
.
b) The given differential equation is: 
The characteristic equation is given by:
, where a=7, b=14 and c=-14
This implies that:


The auxiliary equation is of the form:
where A and B are constants.
Hence any equation of the form:
is a solution to


c) The given differential equation is: 
The characteristic equation is given by:
, where a=7, b=0 and c=-42
This implies that:


The auxiliary equation is of the form:
where A and B are constants.
Hence any equation of the form:
is a solution to


