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DaniilM [7]
3 years ago
7

Hey please help me answer this and explain your answer :) Will give brainlst.

Mathematics
1 answer:
djyliett [7]3 years ago
3 0

Answer:

B for banana

Step-by-step explanation:

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The Redhorse Osaka Wheel, a ferris wheel in Japan, is an amazing 404 feet high. The London Eye, a ferris wheel in England, is 39
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Given the system
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Find a particular solution to the differential equation y′′+2y′+y=2t2−t+3e−2t. y′′+2y′+y=2t2−t+3e−2t.
Jlenok [28]
y''+2y'+y=2t^2-t+3e^{-2t}

The characteristic equation is

r^2+2r+1=(r+1)^2=0\implies r=-1

so the characteristic solution is

y_c=C_1e^{-t}+C_2te^{-t}

For the particular solution, we can try looking for a solution of the form

y_p=at^2+bt+c+de^{-2t}
\implies{y_p}'=2at+b-2de^{-2t}
\implies{y_p}''=2a+4de^{-2t}

Substituting into the ODE, we have

(2a+4de^{-2t})+2(2at+b-2de^{-2t})+(at^2+bt+c+de^{-2t})=2t^2-t+3e^{-2t}
at^2+(4a+b)t+(2a+2b+c)+de^{-2t}=2t^2-t+3e^{-2t}
\implies\begin{cases}a=2\\4a+b=-1\\2a+2b+c=0\\d=3\end{cases}\implies a=2,b=-9,c=14,d=3

So the general solution to the ODE is

y=y_c+y_p
y=C_1e^{-t}+C_2te^{-t}+2t^2-9t+14+3e^{-2t}
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3 years ago
Plzz help with my test
Aleksandr [31]
Y = 4

when you look at the -3 at the x-axis, it meets 4 at the y-axis
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3 years ago
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