Mixing
Nonlinear differential equation with imaginary number coefficient
0
$begingroup$
Let $p$ be a polynomial. Does the differential equation,
$dy/dt=i cdot p(y)$, with initial condition $y(0)=1$ always have a global solution (for all $t in mathbb R$)?
ordinary-differential-equations
asked Jan 21 at 0:34
Craig FeinsteinCraig Feinstein
387321
$endgroup$
add a comment |
0
$begingroup$
Let $p$ be a polynomial. Does the differential equation,
$dy/dt=i cdot p(y)$, with initial condition $y(0)=1$ always have a global solution (for all $t in mathbb R$)?
ordinary-differential-equations
asked Jan 21 at 0:34
Craig FeinsteinCraig Feinstein
387321
$endgroup$
$begingroup$
Does $p$ have complex coefficients or only real ones? You can split both $y$ and $p$ into their real and imaginary parts, to obtain a first-order system for $mathrm{Re}(y)$ and $mathrm{Im}(y)$. To this system you can apply Picard-Lindelöf.
$endgroup$
– Christoph
Jan 21 at 7:13
$begingroup$
I was thinking p has real coefficients.
$endgroup$
– Craig Feinstein
Jan 21 at 12:47
add a comment |
0
0
0
$begingroup$
Let $p$ be a polynomial. Does the differential equation,
$dy/dt=i cdot p(y)$, with initial condition $y(0)=1$ always have a global solution (for all $t in mathbb R$)?
ordinary-differential-equations
asked Jan 21 at 0:34
Craig FeinsteinCraig Feinstein
387321
$endgroup$
Let $p$ be a polynomial. Does the differential equation,
$dy/dt=i cdot p(y)$, with initial condition $y(0)=1$ always have a global solution (for all $t in mathbb R$)?
ordinary-differential-equations
ordinary-differential-equations
asked Jan 21 at 0:34
Craig FeinsteinCraig Feinstein
387321
asked Jan 21 at 0:34
Craig FeinsteinCraig Feinstein
387321
asked Jan 21 at 0:34
Craig FeinsteinCraig Feinstein
387321
asked Jan 21 at 0:34
Craig FeinsteinCraig Feinstein
387321
asked Jan 21 at 0:34
Craig FeinsteinCraig Feinstein
387321
387321
$begingroup$
Does $p$ have complex coefficients or only real ones? You can split both $y$ and $p$ into their real and imaginary parts, to obtain a first-order system for $mathrm{Re}(y)$ and $mathrm{Im}(y)$. To this system you can apply Picard-Lindelöf.
$endgroup$
– Christoph
Jan 21 at 7:13
$begingroup$
I was thinking p has real coefficients.
$endgroup$
– Craig Feinstein
Jan 21 at 12:47
add a comment |
$begingroup$
Does $p$ have complex coefficients or only real ones? You can split both $y$ and $p$ into their real and imaginary parts, to obtain a first-order system for $mathrm{Re}(y)$ and $mathrm{Im}(y)$. To this system you can apply Picard-Lindelöf.
$endgroup$
– Christoph
Jan 21 at 7:13
$begingroup$
I was thinking p has real coefficients.
$endgroup$
– Craig Feinstein
Jan 21 at 12:47
$begingroup$
Does $p$ have complex coefficients or only real ones? You can split both $y$ and $p$ into their real and imaginary parts, to obtain a first-order system for $mathrm{Re}(y)$ and $mathrm{Im}(y)$. To this system you can apply Picard-Lindelöf.
$endgroup$
– Christoph
Jan 21 at 7:13
$begingroup$
Does $p$ have complex coefficients or only real ones? You can split both $y$ and $p$ into their real and imaginary parts, to obtain a first-order system for $mathrm{Re}(y)$ and $mathrm{Im}(y)$. To this system you can apply Picard-Lindelöf.
$endgroup$
– Christoph
Jan 21 at 7:13
$begingroup$
I was thinking p has real coefficients.
$endgroup$
– Craig Feinstein
Jan 21 at 12:47
$begingroup$
I was thinking p has real coefficients.
$endgroup$
– Craig Feinstein
Jan 21 at 12:47
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
});
}
});
draft saved
draft discarded
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%2f3081333%2fnonlinear-differential-equation-with-imaginary-number-coefficient%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
draft saved
draft discarded
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.
draft saved
draft discarded
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%2f3081333%2fnonlinear-differential-equation-with-imaginary-number-coefficient%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
$begingroup$
Does $p$ have complex coefficients or only real ones? You can split both $y$ and $p$ into their real and imaginary parts, to obtain a first-order system for $mathrm{Re}(y)$ and $mathrm{Im}(y)$. To this system you can apply Picard-Lindelöf.
$endgroup$
– Christoph
Jan 21 at 7:13
$begingroup$
I was thinking p has real coefficients.
$endgroup$
– Craig Feinstein
Jan 21 at 12:47