Complete solution vs General solution of a PDE
$begingroup$
I am unable to understand why the general solution is a "bigger set of solutions" than the complete solution.
What is the intuition behind this?
Source of the quotation:
pde
asked Mar 19 '18 at 8:20
AJ_AJ_
5511
$endgroup$
add a comment |
$begingroup$
I am unable to understand why the general solution is a "bigger set of solutions" than the complete solution.
What is the intuition behind this?
Source of the quotation:
pde
asked Mar 19 '18 at 8:20
AJ_AJ_
5511
$endgroup$
add a comment |
$begingroup$
I am unable to understand why the general solution is a "bigger set of solutions" than the complete solution.
What is the intuition behind this?
Source of the quotation:
pde
asked Mar 19 '18 at 8:20
AJ_AJ_
5511
$endgroup$
I am unable to understand why the general solution is a "bigger set of solutions" than the complete solution.
What is the intuition behind this?
Source of the quotation:
pde
pde
asked Mar 19 '18 at 8:20
AJ_AJ_
5511
asked Mar 19 '18 at 8:20
AJ_AJ_
5511
asked Mar 19 '18 at 8:20
AJ_AJ_
5511
asked Mar 19 '18 at 8:20
AJ_AJ_
5511
asked Mar 19 '18 at 8:20
AJ_AJ_
5511
5511
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The general solution involves arbitrary function of known function's $u$ and $v$, while the complete solution involves arbitrary constants.
The arbitrary function is more general than arbitrary constants as it include all possible functions of variable and constants, so I think that's the reason.
edited Dec 18 '18 at 17:56
dantopa
6,51942244
answered Dec 18 '18 at 17:28
Mansoor KhanMansoor Khan
1
$endgroup$
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%2f2698445%2fcomplete-solution-vs-general-solution-of-a-pde%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
$begingroup$
The general solution involves arbitrary function of known function's $u$ and $v$, while the complete solution involves arbitrary constants.
The arbitrary function is more general than arbitrary constants as it include all possible functions of variable and constants, so I think that's the reason.
edited Dec 18 '18 at 17:56
dantopa
6,51942244
answered Dec 18 '18 at 17:28
Mansoor KhanMansoor Khan
1
$endgroup$
add a comment |
$begingroup$
The general solution involves arbitrary function of known function's $u$ and $v$, while the complete solution involves arbitrary constants.
The arbitrary function is more general than arbitrary constants as it include all possible functions of variable and constants, so I think that's the reason.
edited Dec 18 '18 at 17:56
dantopa
6,51942244
answered Dec 18 '18 at 17:28
Mansoor KhanMansoor Khan
1
$endgroup$
add a comment |
$begingroup$
The general solution involves arbitrary function of known function's $u$ and $v$, while the complete solution involves arbitrary constants.
The arbitrary function is more general than arbitrary constants as it include all possible functions of variable and constants, so I think that's the reason.
edited Dec 18 '18 at 17:56
dantopa
6,51942244
answered Dec 18 '18 at 17:28
Mansoor KhanMansoor Khan
1
$endgroup$
The general solution involves arbitrary function of known function's $u$ and $v$, while the complete solution involves arbitrary constants.
The arbitrary function is more general than arbitrary constants as it include all possible functions of variable and constants, so I think that's the reason.
edited Dec 18 '18 at 17:56
dantopa
6,51942244
answered Dec 18 '18 at 17:28
Mansoor KhanMansoor Khan
1
edited Dec 18 '18 at 17:56
dantopa
6,51942244
edited Dec 18 '18 at 17:56
dantopa
6,51942244
edited Dec 18 '18 at 17:56
dantopa
6,51942244
6,51942244
answered Dec 18 '18 at 17:28
Mansoor KhanMansoor Khan
1
answered Dec 18 '18 at 17:28
Mansoor KhanMansoor Khan
1
answered Dec 18 '18 at 17:28
Mansoor KhanMansoor Khan
1
1
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%2f2698445%2fcomplete-solution-vs-general-solution-of-a-pde%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
