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kolbaska11 [484]
3 years ago
8

HELP PLEASE Knanajaj

Mathematics
1 answer:
trapecia [35]3 years ago
5 0

Answer:

35

Step-by-step explanation:

35

35

35

35

35

35

35

35

35

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Put the differential equation 9ty+ety′=yt2+81 into the form y′+p(t)y=g(t) and find p(t) and g(t). p(t)= help (formulas) g(t)= he
alexgriva [62]

Answer:

p(t) = \frac{9t^{3} + 729t  - 1}{e^{t}(t^{2} + 81) }

g(t) = 0

And

The differential equation 9ty + e^{t}y' = \frac{y}{t^{2} + 81 } is  linear and homogeneous

Step-by-step explanation:

Given that,

The differential equation is -

9ty + e^{t}y' = \frac{y}{t^{2} + 81 }

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

By comparing with y′+p(t)y=g(t), we get

p(t) = \frac{9t^{3} + 729t  - 1}{e^{t}(t^{2} + 81) }

g(t) = 0

And

The differential equation 9ty + e^{t}y' = \frac{y}{t^{2} + 81 } is  linear and homogeneous.

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Answer:

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Step-by-step explanation:

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3000/100 =

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30

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3 years ago
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