Answer:
A) Particular solution:

B) Homogeneous solution:

C) The most general solution is

Step-by-step explanation:
Given non homogeneous ODE is

To find homogeneous solution:

To find particular solution:

Substituting
in (1)

Equating the coefficients

The general solution is

from (2) ad (3)

Looks good! You have the right answers.
However, the graph for 12 and 15 is inaccurate! Because he starts from a stop sign/stop light, the graph's speed should start from the origin!
Not to confuse you or anything, but this means the graph does not follow the description of the problem. Please let your teacher know so s/he can fix the worksheet.
Answer:
3. They're adding by 5 so,
Step-by-step explanation: