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
Scilla [17]
3 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:
MrMuchimi3 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}

You might be interested in
I need help finding the answer
11111nata11111 [884]

Answer:

a

Step-by-step explanation:


8 0
3 years ago
I am really stuck for how to solve x with algebra it is so confusing does anyone have any tips
MAXImum [283]
<span>Example: x − 2 = 4</span>

When we put 6 in place of x we get:

6 − 2 = 4

which is true

So x = 6 is a solution.

8 0
3 years ago
Community Gym charges a $60 membership fee and a $60 monthly fee. Workout Gym charges a $200 membership fee and a $50 monthly fe
Kitty [74]

Answer:

14 months

Step-by-step explanation:

60x+60=50x+200

10x+60=200

10x=140

x=14

60(14)+60=900

50(14)+200=900

8 0
3 years ago
I will be back to help everyone bye,vale,adios i forgot how to say it in french
kupik [55]

Answer:

Huh I am confused

Step-by-step explanation:

Do you need help with anything

4 0
3 years ago
Read 2 more answers
Isabel is using the TVM Solver on her graphing calculator as shown below to determine how much she has to invest now in a saving
Finger [1]

Answer:

C monthly

Step-by-step explanation:

Apex

3 0
3 years ago
Other questions:
  • Math question please help <br> If you get this right I will mark you as a brainliest
    5·1 answer
  • If Oliver withdraws $285.10 from his savings account to make the purchase, how much would he have earned in interest on that amo
    7·1 answer
  • What is the value of the 9 in 913256
    8·2 answers
  • I need help please. The picture
    8·2 answers
  • REAL ANSWER FOR BOTH OF THEM PLEASE THERES MORE POINTS ON THIS ONE
    11·2 answers
  • 3. Find the measure of each anglo in the diagram above.
    7·1 answer
  • PLEASE HELP ME
    14·2 answers
  • 6 1/2 divided by 3 2/3
    8·2 answers
  • darius and dakota re roommates. together they have 238 books. if darius has 50 more books than dakota, how many books does dakot
    15·1 answer
  • Hii!
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!