1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
balandron [24]
2 years ago
12

Solve the given integral equation for LaTeX: y(t)y ( t ). LaTeX: y(t)+9\displaystyle{\int_{0}^{t}e^{9(t-v)}y(v)\, dv}=\sin(3t)y

( t ) + 9 ∫ 0 t e 9 ( t − v ) y ( v ) d v = sin ⁡ ( 3 t ) Group of answer choices LaTeX: y(t)=3\cos(3t)+9\sin(3t)-9 y ( t ) = 3 cos ⁡ ( 3 t ) + 9 sin ⁡ ( 3 t ) − 9 LaTeX: y(t)=3\cos(3t)+\sin(3t)-3 y ( t ) = 3 cos ⁡ ( 3 t ) + sin ⁡ ( 3 t ) − 3 LaTeX: y(t)=3\cos(3t)+\sin(3t) y ( t ) = 3 cos ⁡ ( 3 t ) + sin ⁡ ( 3 t ) LaTeX: y(t)=3\cos(3t)+9\sin(3t) y ( t ) = 3 cos ⁡ ( 3 t ) + 9 sin ⁡ ( 3 t ) LaTeX: y(t)=\cos(3t)+3\sin(3t)-3
Mathematics
1 answer:
choli [55]2 years ago
6 0

Looks like the equation is

y(t)+9\displaystyle\int_0^te^{9(t-v)}y(v)\,\mathrm dv=\sin(3t)

Differentiating both sides yields the linear ODE,

y'(t)+9e^{9(t-t)}y(t)=3\cos(3t)

or

y'(t)+9y(t)=3\cos(3t)

Multiply both sides by the integrating factor e^{9t}:

e^{9t}y'(t)+9e^{9t}y(t)=3e^{9t}\cos(3t)

\left(e^{9t}y(t)\right)'=3e^{9t}\cos(3t)

Integrate both sides, then solve for y(t):

e^{9t}y(t)=\dfrac1{10}e^{9t}(\sin(3t)+3\cos(3t))+C

y(t)=\dfrac{\sin(3t)+3\cos(3t)}{10}+Ce^{-9t}

The given answer choices all seem to be missing <em>C</em>, so I suspect you left out an initial condition. But we can find one; let t=0, then the integral vanishes and we're left with y(0)=0. So

0=\dfrac{0+3}{10}+C\implies C=-\dfrac3{10}

So the particular solution is

y(t)=\dfrac{\sin(3t)+3\cos(3t)-3e^{-9t}}{10}

You might be interested in
PLEASE ANSWER ASAP,
Vlad1618 [11]
That is correct (10)   Rate = 40/4 = 10 ft / s
5 0
3 years ago
List least to greatest <br> -3/8, 5/16, -0.65, 2/4
amid [387]
-0.65
-3/8
2/4
5/16
I hope this is right, the negatives should go first because you are taking away, then positives 
8 0
3 years ago
(8√2 - 5) (9√5 +6√10)<br> Simplify
salantis [7]

Answer:

42 (square root>) 10 + 51 (square root>) 5

Step-by-step explanation:

5 0
2 years ago
Factor the equation: 25x^2-5xy-5xy^2+y^3-y^2
lianna [129]

Answer:

−5xy^2+y^3+25x^2−5xy−y^2

Step-by-step explanation:

25x^2−5xy−5xy^2+y^3−y^2=

25x^2−5xy−2

———————————-

7 0
3 years ago
The diameter of Jupiter is 88,732 miles. The 8 in the ten thousands place is how many times greater than the 8 in the thousands
pshichka [43]
1000 times greater than that
6 0
3 years ago
Other questions:
  • The base of a prism is a right triangle with a base and height measurement of 12cm and a 5cm. If the volume of the prism is 210c
    7·2 answers
  • Can someone help please ?!!
    11·1 answer
  • Your employer pays 75% of your health insurance premium. If the annual premium is $2530, and you are paid weekly, how much is de
    8·2 answers
  • The population of a city in 2005 was 15,000. By 2015, the city's population had grown to 45,000 people. Assuming that the popula
    13·1 answer
  • Hello, here's the question :D
    10·1 answer
  • Will give brainlest answer
    6·1 answer
  • The diagram shows an equilateral triangle, a square, and one diagonal of the square. what is the value of x
    13·1 answer
  • Is the sequence 4, 8, 12, 16, 20, ... a geometric sequence? If it is a geometric sequence, what is the common ratio?
    15·1 answer
  • POSSIBLE POINTS: 8
    13·1 answer
  • Select all the answers choices that would NOT be part of the domain of f o g(x) if:
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!