In a pursuit problem, the target moves along a given curve,
$begingroup$
In a pursuit problem, the target moves along a given curve, another object, the pursuer pursues the first, that is, at all times the pursuer moves in the direction of the target.
Suppose that the target is a ship that moves along a straight line and that the pursuer is a destroyer that moves so that the distance between it and the ship is constant, but it is $a> 0 $
a) If $(x, 0) $ represents the position of the ship at a given moment and $y (x) $ is the ordinate of the position of the destroyer at that same moment, deduce that $y$ satisfies the following initial value problem: $$left {begin{array}{c} y'(x) = - dfrac{y (x)}{sqrt{a^{2} -y^{ 2}(x)}} \ y(0) = a end{array}right. $$
b) Show that the previous problem has a unique solution,
I have problems with the first literal because, I do not know what it is that I am asking ... and for the second one, how do I demonstrate the uniqueness of the solution?
real-analysis calculus ordinary-differential-equations
asked Dec 5 '18 at 21:36
Santiago SeekerSantiago Seeker
618
$endgroup$
add a comment |
$begingroup$
In a pursuit problem, the target moves along a given curve, another object, the pursuer pursues the first, that is, at all times the pursuer moves in the direction of the target.
Suppose that the target is a ship that moves along a straight line and that the pursuer is a destroyer that moves so that the distance between it and the ship is constant, but it is $a> 0 $
a) If $(x, 0) $ represents the position of the ship at a given moment and $y (x) $ is the ordinate of the position of the destroyer at that same moment, deduce that $y$ satisfies the following initial value problem: $$left {begin{array}{c} y'(x) = - dfrac{y (x)}{sqrt{a^{2} -y^{ 2}(x)}} \ y(0) = a end{array}right. $$
b) Show that the previous problem has a unique solution,
I have problems with the first literal because, I do not know what it is that I am asking ... and for the second one, how do I demonstrate the uniqueness of the solution?
real-analysis calculus ordinary-differential-equations
asked Dec 5 '18 at 21:36
Santiago SeekerSantiago Seeker
618
$endgroup$
add a comment |
$begingroup$
In a pursuit problem, the target moves along a given curve, another object, the pursuer pursues the first, that is, at all times the pursuer moves in the direction of the target.
Suppose that the target is a ship that moves along a straight line and that the pursuer is a destroyer that moves so that the distance between it and the ship is constant, but it is $a> 0 $
a) If $(x, 0) $ represents the position of the ship at a given moment and $y (x) $ is the ordinate of the position of the destroyer at that same moment, deduce that $y$ satisfies the following initial value problem: $$left {begin{array}{c} y'(x) = - dfrac{y (x)}{sqrt{a^{2} -y^{ 2}(x)}} \ y(0) = a end{array}right. $$
b) Show that the previous problem has a unique solution,
I have problems with the first literal because, I do not know what it is that I am asking ... and for the second one, how do I demonstrate the uniqueness of the solution?
real-analysis calculus ordinary-differential-equations
asked Dec 5 '18 at 21:36
Santiago SeekerSantiago Seeker
618
$endgroup$
In a pursuit problem, the target moves along a given curve, another object, the pursuer pursues the first, that is, at all times the pursuer moves in the direction of the target.
Suppose that the target is a ship that moves along a straight line and that the pursuer is a destroyer that moves so that the distance between it and the ship is constant, but it is $a> 0 $
a) If $(x, 0) $ represents the position of the ship at a given moment and $y (x) $ is the ordinate of the position of the destroyer at that same moment, deduce that $y$ satisfies the following initial value problem: $$left {begin{array}{c} y'(x) = - dfrac{y (x)}{sqrt{a^{2} -y^{ 2}(x)}} \ y(0) = a end{array}right. $$
b) Show that the previous problem has a unique solution,
I have problems with the first literal because, I do not know what it is that I am asking ... and for the second one, how do I demonstrate the uniqueness of the solution?
real-analysis calculus ordinary-differential-equations
real-analysis calculus ordinary-differential-equations
asked Dec 5 '18 at 21:36
Santiago SeekerSantiago Seeker
618
asked Dec 5 '18 at 21:36
Santiago SeekerSantiago Seeker
618
asked Dec 5 '18 at 21:36
Santiago SeekerSantiago Seeker
618
asked Dec 5 '18 at 21:36
Santiago SeekerSantiago Seeker
618
asked Dec 5 '18 at 21:36
Santiago SeekerSantiago Seeker
618
618
add a comment |
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3027683%2fin-a-pursuit-problem-the-target-moves-along-a-given-curve%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3027683%2fin-a-pursuit-problem-the-target-moves-along-a-given-curve%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
