I would use a proportion
51.03/88% = x/100%
Which is saying: if 51.03 is 88% of the number, what is 100% of the number
Cross multiply to get x=57.99
Answer:
![p(t) = \frac{9t^{3} + 729t - 1}{e^{t}(t^{2} + 81) }](https://tex.z-dn.net/?f=p%28t%29%20%3D%20%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)
g(t) = 0
And
The differential equation
is linear and homogeneous
Step-by-step explanation:
Given that,
The differential equation is -
![9ty + e^{t}y' = \frac{y}{t^{2} + 81 }](https://tex.z-dn.net/?f=9ty%20%2B%20e%5E%7Bt%7Dy%27%20%3D%20%5Cfrac%7By%7D%7Bt%5E%7B2%7D%20%2B%2081%20%7D)
![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
![p(t) = \frac{9t^{3} + 729t - 1}{e^{t}(t^{2} + 81) }](https://tex.z-dn.net/?f=p%28t%29%20%3D%20%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)
g(t) = 0
And
The differential equation
is linear and homogeneous.
Step-by-step explanation:
if there are no typos, then the second and the fourth answers are correct.
1 - 1.7 = -0.7 or -2×0.35
-2x = -2(x)