HomeworkLib
Question

Does there exist a unique solution to the following IVP (initial-value-problem) in the neighborhood of the original condition? find all constant solutions. Justify your answers.

ty-ye-y sin(12), y(T)-e

I am having trouble understanding my professors solution where 3leq xleq 4 and 2leq yleq 3 . I understand that pi is between 3 and 4 and e is between 2 and 3 but how to you justify that. Also what good does taking the partial derivative of Y have to do with anything, as that also consists of the solution. f_y=(1-y)e^{-y}sin(x^2)

math   Advanced-Math   
0 0
Add a comment Improve this question Transcribed image text
Next > < Previous
Sort answers by oldest

Homework Answers

Answer #1

Here , we use existence and uniqueness theoram....

dy dys Note noux asi gay une easiy

Any doubt then comment below.. i will explain and clear your doubt..  

0 0
Add a comment
Know the answer?
Add Answer to:
Does there exist a unique solution to the following IVP (initial-value-problem) in the neighborhood of the...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions

  • 9. (4 points) Does there exist a unique solution to the following IVP in a neighborhood...

    9. (4 points) Does there exist a unique solution to the following IVP in a neighborhood of the initial condition? Find all constant solutions, if any. Specify the largest interval over which your constant solution is valid. Justify your answers. dy (ey-)(tan y) In(1 -),y(0)-3/2 9. (4 points) Does there exist a unique solution to the following IVP in a neighborhood of the initial condition? Find all constant solutions, if any. Specify the largest interval over which your constant solution...

  • Consider the IVP, 1. Apply the Fundamental Existence and Uniqueness Theorem to show that a solution...

    Consider the IVP, 1. Apply the Fundamental Existence and Uniqueness Theorem to show that a solution exists. 2. Use the Runge-Kutta method with various step-sizes to estimate the maximum t-value, , for which the solution is defined on the interval . Include a few representative graphs with your submission, and the lists of points. 3. Find the exact solution to the IVP and solve for analytically. How close was your approximation from the previous question? 4. The Runge-Kutta method continues...

  • 1. [5 Consider the IVP rty(t) + 2 sin(t)y(t) = tan(t) y(5)=2 Does a unique solution of the IVP ex...

    pls do all questions. thanx 1. [5 Consider the IVP rty(t) + 2 sin(t)y(t) = tan(t) y(5)=2 Does a unique solution of the IVP exist? Do not solve the IVP but fully justify you answer. What is the IOE? 2. 4 Consider the ODE Using undetermined coefficients, what is an approprite guess for the coefficient (s) in yp but fully justify you answer. ? Do not solve for 3. [10] Solve the IVP. Use any approach you like y(x) 6y'(x)...

  • (A) Find the largest x-interval where the initial value problem has a unique solution: Where A,...

    (A) Find the largest x-interval where the initial value problem has a unique solution: Where A, B, C, D, E, F are some known constants. (B) Determine whether the set of functions could form a fundamental set of solution of a linear differential equation Thank you We were unable to transcribe this image5, sinx, cos2.c

  • Consider the initial value problem below has a series solution centered at zero of y =...

    Consider the initial value problem below has a series solution centered at zero of y = (x). Determine '(0), ''(0) and 4(0). y''+ x2y'+ cos(x)y = 0, y(0) = 2, y'(0) = 3. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image

  • Multiple Choice: Let A = . Let x be the solution of the following initial value...

    Multiple Choice: Let A = . Let x be the solution of the following initial value problem: x' = Ax, x(0) = . What is the value of ln(x())? (a)    (b)    (c)    (d)    (e) We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this...

  • Which of the following is the solution to the differential equation with the initial condition y(1)...

    Which of the following is the solution to the differential equation with the initial condition y(1) = -1/2 A. B. C. D. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image

  • [7] 1. Consider the initial value problem (IVP) y′(t) = −y(t), y(0) = 1 The solution to this IVP ...

    [7] 1. Consider the initial value problem (IVP) y′(t) = −y(t), y(0) = 1 The solution to this IVP is y(t) = e−t [1] i) Implement Euler’s method and generate an approximate solution of this IVP over the interval [0,2], using stepsize h = 0.1. (The Google sheet posted on LEARN is set up to carry out precisely this task.) Report the resulting approximation of the value y(2). [1] ii) Repeat part (ii), but use stepsize h = 0.05. Describe...

  • For each initial value problem, does Picards's theorem apply? If so, determine if it guarantees that...

    For each initial value problem, does Picards's theorem apply? If so, determine if it guarantees that a solutio exists and is unique. Theorem (Picard). Consider the initial value problem dy = f(t,y), dt (IVP) y(to) = Yo- (a) Existence: If f(t,y) is continuous in an open rectangle R = {(t,y) |a<t < b, c < y < d} and (to, Yo) belongs in R, then there exist h > 0 and a solution y = y(t) of (IVP) defined in...

  • Given two independent random variables and and a function and given that , does the following...

    Given two independent random variables and and a function and given that , does the following inequality hold? I have tried doing it this way. Now, because and are independent, Is my approach correct? We were unable to transcribe this imageWe were unable to transcribe this imagef(X) We were unable to transcribe this imageax{f(E[X1]), f (E[X2)}<a 2 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT