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Stella [2.4K]
2 years ago
10

Help and please number the answers accurately thanks a lot!

Mathematics
1 answer:
kvasek [131]2 years ago
7 0

Answer:

I KNOWW THE ANSWER!!

Step-by-step explanation:

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HURRY. NEED To be done by 10:30
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<img src="https://tex.z-dn.net/?f=5%28sin%28t%29%20%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%2Bycos%28t%29%29%29%3Dcos%28t%29%20%20%28sin%28
Nataliya [291]
Assuming you mean

5\sin t\dfrac{\mathrm dy}{\mathrm dt}+5y\cos t=\cos t\sin^2t

This ODE is linear in y, and you can already contract the left hand side as the derivative of a product:

\dfrac{\mathrm d}{\mathrm dt}\left[5y\sin t\right]=\cos t\sin^2t

Integrating both sides with respect to t yields

5y\sin t=\displaystyle\int\cos t\sin^2t\,\mathrm dt
5y\sin t=\dfrac13\sin^3t+C
y=\dfrac1{15}\sin^2t+C\csc t

Given that y\left(\dfrac\pi2\right)=9, we have

9=\dfrac1{15}\sin^2\dfrac\pi2+C\csc\dfrac\pi2
9=\dfrac1{15}+C
C=\dfrac{134}{15}

so that the particular solution over the interval is

y=\dfrac1{15}\sin^2t+\dfrac{134}{15}\csc t
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Write an equation that represents the line.
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y = -2x - 3

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