(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:
Answer:
you put two of the equations together and then the last one there you just automatically added on
Step-by-step explanation:
4x-7y=-28
25xy
Answer:
1,2,3,4,5,6 possibilities, so 1,3,5 are odd. 3/6 probability. consecutive rolls mean multiplication. 3/6 times 3/6 times.... a total of 5 times.
Step-by-step explanation:
Answer:
x = 1.5
Step-by-step explanation:
First, we distribute (get rid of parentheses):
6x - 3 - 3x = 5 - x - 2
Then, we simplify:
3x - 3 = 3 - x
Then, we combine like terms:
3x + x = 3 + 3
Then, we simplify again:
4x + 6
Finally, we divide 4 on both sides:
We got x = 1.5
Hope this helps!
Hellllllooooo I hope it help
