Answer:

g(t) = 0
And
The differential equation
is linear and homogeneous
Step-by-step explanation:
Given that,
The differential equation is -

![e^{t}y' + (9t - \frac{1}{t^{2} + 81 } )y = 0\\e^{t}y' + (\frac{9t(t^{2} + 81 ) - 1}{t^{2} + 81 } )y = 0\\e^{t}y' + (\frac{9t^{3} + 729t - 1}{t^{2} + 81 } )y = 0\\y' + [\frac{9t^{3} + 729t - 1}{e^{t}(t^{2} + 81) } ]y = 0](https://tex.z-dn.net/?f=e%5E%7Bt%7Dy%27%20%2B%20%289t%20-%20%5Cfrac%7B1%7D%7Bt%5E%7B2%7D%20%2B%2081%20%7D%20%29y%20%3D%200%5C%5Ce%5E%7Bt%7Dy%27%20%2B%20%28%5Cfrac%7B9t%28t%5E%7B2%7D%20%2B%2081%20%29%20-%201%7D%7Bt%5E%7B2%7D%20%2B%2081%20%7D%20%29y%20%3D%200%5C%5Ce%5E%7Bt%7Dy%27%20%2B%20%28%5Cfrac%7B9t%5E%7B3%7D%20%2B%20729t%20%20-%201%7D%7Bt%5E%7B2%7D%20%2B%2081%20%7D%20%29y%20%3D%200%5C%5Cy%27%20%2B%20%5B%5Cfrac%7B9t%5E%7B3%7D%20%2B%20729t%20%20-%201%7D%7Be%5E%7Bt%7D%28t%5E%7B2%7D%20%2B%2081%29%20%7D%20%5Dy%20%3D%200)
By comparing with y′+p(t)y=g(t), we get

g(t) = 0
And
The differential equation
is linear and homogeneous.
Answer:
x = 37
Step-by-step explanation:
Answer:
The answer would be 2012 and 2004
Step-by-step explanation:
when you round 30.346 to the nearest tenth it is 30.4 and when you round 30.406 to the nearest tenth then it is also 30.4.
Hope it helps!
:)
Answer:
686.27
Step-by-step explanation:
x + .02x = 700
1.02x = 700
x = 686.27
Answer:
y – 2 = (x – 3)
Step-by-step explanation:
because (3, 2) was the point used for the equation but turned negative because you need to make it negative for the equation. y - y1 =m(x - x1)