Answer:
28,550.33333
Step-by-step explanation:
28,550.33333 + 3 = 28,553.33333
28,553.33333 x 3 = 85,659.99999
85,659.99999 ÷ 2 = 42830
 
        
             
        
        
        
Answer:
?????????????????
Step-by-step explanation:
????????
 
        
             
        
        
        
You just need to divide 13 and 2 and get 6.5.
        
             
        
        
        
(a) Take the Laplace transform of both sides:


where the transform of  comes from
 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.
 is one solution to the original ODE.

Substitute these into the ODE to see everything checks out:
