Match each differential equation to a function which is a solution.
functions
a. y=3x+x2y=3x+x2,
b. y=e−4xy=e−4x,
c. y=sin(x)y=sin⁡(x),
d. y=x12y=x12,
e. y=6e3xy=6e3x,

differential equations

1. y″+y=0y″+y=0
2. y′=3yy′=3y
3. 2x2y″+3xy′=y2x2y″+3xy′=y
4. y″+6y′+8y=0y″+6y′+8y=0

1 - C

2 - E

3 - no answer

4 - B

Step-by-step explanation:

A.

So, A is not an answer for 1

So, A is not an answer for 2

So, A is not an answer for 3

So, A is not an answer for 4

B.

So, B is not an answer for 1

So, B is not an answer for 2

So, B is not an answer for 3

So, B is an answer for 4

C.

So, C is an answer for 1

We jump to

D.

So, D is not an answer for 2

So, D is not an answer for 3

E.

So, E is an answer for 2

answer

see attachment

explanation

the given function is

this function has y-intercept at

-4 and a slope of 2.

note that, the graph has a positive slope.

the graph that represents this function is the straight line that moves upward from left to right.

the graph touches the y-axis at -4.

the correct choice is the graph shown in the attachment.