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Scilla [17]
4 years ago
8

Find a closed-form solution to the integral equation y(x) = 3 + Z x e dt ty(t) , x > 0. In other words, express y(x) as a fun

ction that doesn’t involve an integral. (Hint: Use the Fundamental Theorem of Calculus to obtain a differential equation. You can find an initial condition by evaluating the original integral equation at a strategic value of x.)
Mathematics
1 answer:
MrMuchimi4 years ago
8 0

Answer:

y{x} = \sqrt{7+2Inx}

Step-by-step explanation:

y(x)= 3 + \int\limits^x_e {dx}/ \, ty(t) , x>0}

Let say; By y(x)= y(e)  

we have;  

y(e)= 3 + \int\limits^e_e {dt}/ \, ty= 3+0

Using Fundamental Theorem of Calculus and differentiating by Lebiniz Rule:

y^{1} (x) = 0 + 1/ xy

y^{1} = 1/xy  

dy/dx = 1/xy  

\int\limits {y} \, dxy = \int\limits \, dx/x

y^{2}/2 Inx + C

RECALL: y(e) = 3  

(3)^{2} / 2 = In (e) + C  

\frac{9}{2} =In(e)+C  

\frac{9}{2} - 1 = C

\frac{7}{2} = C  

y^{2} / 2 = In x +C

y^{2} / 2 = In x +7/2

MULTIPLYING BOTH SIDE BY 2 , TO ELIMINATE THE DENOMINATOR, WE HAVE;

y^{2} = {7+2Inx}  

y{x} = \sqrt{7+2Inx}

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Step-by-step explanation:

Let the length be L.

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So, we are given that

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So, according to the Question,

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4 years ago
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3 years ago
Newton’s Law of Cooling expresses the relationship between the temperature of a cooling object y and the time t elapsed since co
True [87]

Answer:

79 °F

Step-by-step explanation:

Newton’s Law of Cooling:

y = ae^{-kt} + c

Data

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4 0
4 years ago
Read 2 more answers
68. Solve: 46x - 10) = 8x + 40<br>A 0<br>B.5/2<br>ina<br>c. 23<br>D. 5​
Artist 52 [7]

Solve: 4(6x - 10) = 8x + 40

A 0

B.5/2

c. 23

D. 5​

<h3><u>Answer:</u></h3>

Option D

The solution to given equation is x = 5

<h3><u>Solution:</u></h3>

Given that we have to solve the given equation

4(6x - 10) = 8x + 40

Let us solve the above expression and find value of "x"

Multiplying 4 with terms inside bracket in L.H.S we get,

24x - 40 = 8x + 40

Move the variables to one side and constant terms to other side

24x - 8x = 40 + 40

Combine the like terms,

16x = 80

x = \frac{80}{16} = 5

Thus solution to given equation is x = 5

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4 years ago
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lisov135 [29]

Step-by-step explanation:

C is less than 5

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7 0
2 years ago
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