Euler Equations having double roots solutions
$begingroup$
If the Euler equation have the double roots as a solution, second solution will be $y_2(x)=x^rln{x}$. What is its proof? or how it can be derived? To find a second solution,we will use the fact that constant times the solution is also a solution to linear homogeneous differential equations. Now why do we choose $ln{x}$ as constant?why not any other constant?
ordinary-differential-equations self-learning
asked Dec 19 '18 at 6:56
Dhamnekar WinodDhamnekar Winod
392414
$endgroup$
add a comment |
$begingroup$
If the Euler equation have the double roots as a solution, second solution will be $y_2(x)=x^rln{x}$. What is its proof? or how it can be derived? To find a second solution,we will use the fact that constant times the solution is also a solution to linear homogeneous differential equations. Now why do we choose $ln{x}$ as constant?why not any other constant?
ordinary-differential-equations self-learning
asked Dec 19 '18 at 6:56
Dhamnekar WinodDhamnekar Winod
392414
$endgroup$
add a comment |
$begingroup$
If the Euler equation have the double roots as a solution, second solution will be $y_2(x)=x^rln{x}$. What is its proof? or how it can be derived? To find a second solution,we will use the fact that constant times the solution is also a solution to linear homogeneous differential equations. Now why do we choose $ln{x}$ as constant?why not any other constant?
ordinary-differential-equations self-learning
asked Dec 19 '18 at 6:56
Dhamnekar WinodDhamnekar Winod
392414
$endgroup$
If the Euler equation have the double roots as a solution, second solution will be $y_2(x)=x^rln{x}$. What is its proof? or how it can be derived? To find a second solution,we will use the fact that constant times the solution is also a solution to linear homogeneous differential equations. Now why do we choose $ln{x}$ as constant?why not any other constant?
ordinary-differential-equations self-learning
ordinary-differential-equations self-learning
asked Dec 19 '18 at 6:56
Dhamnekar WinodDhamnekar Winod
392414
asked Dec 19 '18 at 6:56
Dhamnekar WinodDhamnekar Winod
392414
edited Dec 19 '18 at 8:46
Dhamnekar Winod
asked Dec 19 '18 at 6:56
Dhamnekar WinodDhamnekar Winod
392414
asked Dec 19 '18 at 6:56
Dhamnekar WinodDhamnekar Winod
392414
asked Dec 19 '18 at 6:56
Dhamnekar WinodDhamnekar Winod
392414
392414
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
One can find answer to this question here$rightarrow$[Euler equation having double roots or repeated roots as a solution1DE]
answered Dec 20 '18 at 7:19
Dhamnekar WinodDhamnekar Winod
392414
$endgroup$
add a comment |
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%2f3046113%2feuler-equations-having-double-roots-solutions%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
One can find answer to this question here$rightarrow$[Euler equation having double roots or repeated roots as a solution1DE]
answered Dec 20 '18 at 7:19
Dhamnekar WinodDhamnekar Winod
392414
$endgroup$
add a comment |
$begingroup$
One can find answer to this question here$rightarrow$[Euler equation having double roots or repeated roots as a solution1DE]
answered Dec 20 '18 at 7:19
Dhamnekar WinodDhamnekar Winod
392414
$endgroup$
add a comment |
$begingroup$
One can find answer to this question here$rightarrow$[Euler equation having double roots or repeated roots as a solution1DE]
answered Dec 20 '18 at 7:19
Dhamnekar WinodDhamnekar Winod
392414
$endgroup$
One can find answer to this question here$rightarrow$[Euler equation having double roots or repeated roots as a solution1DE]
answered Dec 20 '18 at 7:19
Dhamnekar WinodDhamnekar Winod
392414
edited Dec 21 '18 at 5:20
answered Dec 20 '18 at 7:19
Dhamnekar WinodDhamnekar Winod
392414
answered Dec 20 '18 at 7:19
Dhamnekar WinodDhamnekar Winod
392414
answered Dec 20 '18 at 7:19
Dhamnekar WinodDhamnekar Winod
392414
392414
add a comment |
add a comment |
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%2f3046113%2feuler-equations-having-double-roots-solutions%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
