Answer:
wheres the question? it just says what you said-
(a) Take the Laplace transform of both sides:


where the transform of
comes from
![L[ty'(t)]=-(L[y'(t)])'=-(sY(s)-y(0))'=-Y(s)-sY'(s)](https://tex.z-dn.net/?f=L%5Bty%27%28t%29%5D%3D-%28L%5By%27%28t%29%5D%29%27%3D-%28sY%28s%29-y%280%29%29%27%3D-Y%28s%29-sY%27%28s%29)
This yields the linear ODE,

Divides both sides by
:

Find the integrating factor:

Multiply both sides of the ODE by
:

The left side condenses into the derivative of a product:

Integrate both sides and solve for
:


(b) Taking the inverse transform of both sides gives
![y(t)=\dfrac{7t^2}2+C\,L^{-1}\left[\dfrac{e^{s^2}}{s^3}\right]](https://tex.z-dn.net/?f=y%28t%29%3D%5Cdfrac%7B7t%5E2%7D2%2BC%5C%2CL%5E%7B-1%7D%5Cleft%5B%5Cdfrac%7Be%5E%7Bs%5E2%7D%7D%7Bs%5E3%7D%5Cright%5D)
I don't know whether the remaining inverse transform can be resolved, but using the principle of superposition, we know that
is one solution to the original ODE.

Substitute these into the ODE to see everything checks out:

They're all d).
1) 28>24=10+14
2) Either 96/8=? or 8*?=96 describe the problem, ? being the number of chairs (the blank square in the answers). Of the two only the first appears in the options.
3) This question is ambiguous: if someone went both days, we could say the total number of people who went to the Saturday and Sunday games would be less than 3271+5844=9115. But who wrote the question likely wanted you to just do the sum between the two numbers, so of all options d is likely what they want you to choose.
15
(2 + 5) - (2 x -4) = 15
7 - -8
Minus a negative goes upwards.
15