Match solutions and differential equations. note: each equation may have more than one solution. select all that apply. (a) 7y'' − 7y = 0 y = ex y = x3 y = e−x y = x−2 (b) 7x2y'' + 14xy' − 14y = 0 y = ex y = x3 y = e−x y = x−2 (c) 7x2y'' − 42y = 0 y = ex y = x3 y = e−x

a-

b-

c-

Step-by-step explanation:

a.7 y''-7 y =0

Auxillary equation

D=1,-1

Then , the solution of given differential equation

2.

Y=

Substitute in the given differential equation

Hence, is not a solution of given differential equation

are also not a solution of given differential equation.

y=

Substitute the values in the differential equation

=

Hence, is a solution of given differential equation.

c.

Substitute the values in the differential equation

Hence, is a solution of given differential equation.

a-

b-

c-

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

ab will be equal to