(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:
Step-by-step explanation:
eq. of line is y-(-2)=-3(x-6)
y+2=-3x+18
y=-3x+18-2
y=-3x+16
∵(a,7) lies on it.
7=-a+16
a=16-7=9
a=9
Answer:
25
Step-by-step explanation:
25 because when you add 12 and 5 then subract the numerator you get 25
If you would like to know which equation relates the weight and the dosage, you can find this using the following steps:
30-pound dog ... 1 milligram of the medicine
w pound dog ... d milligram of the medicine
30 * d = 1 * w
30 * d = w
The correct result would be 30 * d = w.
Answer:
Step-by-step explanation:
congruent angles:
angle A = H
B = J
K = C
L = D
proportional side :
AB proportional HJ
AD proportional HL
JK proportional BC
KL proportional CD
hope it helps
if it does so then please mark me as brainliest