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NISA [10]
2 years ago
12

Write an expression for the

Mathematics
1 answer:
klio [65]2 years ago
8 0

Answer:

8/2 - 20/5

Step-by-step explanation:

please mark brainliest.

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Find the general solution of the following ODE: y' + 1/t y = 3 cos(2t), t > 0.
Margarita [4]

Answer:

y = 3sin2t/2 - 3cos2t/4t + C/t

Step-by-step explanation:

The differential equation y' + 1/t y = 3 cos(2t) is a first order differential equation in the form y'+p(t)y = q(t) with integrating factor I = e^∫p(t)dt

Comparing the standard form with the given differential equation.

p(t) = 1/t and q(t) = 3cos(2t)

I = e^∫1/tdt

I = e^ln(t)

I = t

The general solution for first a first order DE is expressed as;

y×I = ∫q(t)Idt + C where I is the integrating factor and C is the constant of integration.

yt = ∫t(3cos2t)dt

yt = 3∫t(cos2t)dt ...... 1

Integrating ∫t(cos2t)dt using integration by part.

Let u = t, dv = cos2tdt

du/dt = 1; du = dt

v = ∫(cos2t)dt

v = sin2t/2

∫t(cos2t)dt = t(sin2t/2) + ∫(sin2t)/2dt

= tsin2t/2 - cos2t/4 ..... 2

Substituting equation 2 into 1

yt = 3(tsin2t/2 - cos2t/4) + C

Divide through by t

y = 3sin2t/2 - 3cos2t/4t + C/t

Hence the general solution to the ODE is y = 3sin2t/2 - 3cos2t/4t + C/t

3 0
3 years ago
In the equation 5x = 60, what is the next step in the equation solving sequence?
muminat

Answer:

C

Step-by-step explanation:

You have to divide both sides by the coefficient of x

7 0
3 years ago
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A Rectangular Room has a length of 3 more than its width. The perimeter of the room is 90. What is the width of the room?
nignag [31]
The answer to your question is 21
4 0
3 years ago
What is 5/14 simplified ? Need answer ASAP.
iogann1982 [59]

Answer:

5/14

Step-by-step explanation:

5/14 is the simplified form.

6 0
3 years ago
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Steve paid $62 for groceries last week. That was $6.75 more then he spent this week. How much did Steve spend this week?
yarga [219]
the answer is to 62-6.75 is 55.25
6 0
3 years ago
Read 2 more answers
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