(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:
Graph of the inequality x< -3 as shown below in the figure.
Step-by-step explanation:
Given the inequality: x < -3
Graph of this inequality as shown below in the figure.
All the points that are lie in the shaded area satisfy the equation x < -3 or
In other words, we can say that x can take any value less than -3 .
x ≠ -3 or any number that is greater than -3.
Since there is a strict inequality i.e x < -3 , the points that lie on the line x = -3 does not satisfy the equation.
Therefore, the dotted line is marked at x = -3
I think the answer is G=/2.(8) =(G=4)
Answer:
Test A: 40 words per minute
Test B: 54 words per minute
Test C: 44 words per minute
<em><u>Test B has the highest unit rate</u></em>
Step-by-step explanation:
Test A divide 30 by
(30/0.75=40)
Test B divide 78 by
(78/1.5=52)
Test C divide 99 by
(99/2.25=44)
<u>Hope this helps :-)</u>
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