Nonlinear Differential Equation with unknown source
I've encountered this equation:
$$S(t)-y(t)=alpha left(frac{dy(t)}{dt}right)^2$$
where $S(t)$ is a non-defined source (input of our system) and $alpha$ is a positive constant.
I've tried variable separation but without any success.
Please, can someone help me find a solution or a possible approach?
Thanks
differential-equations
edited Nov 30 '18 at 8:03
Dylan
12.4k31026
asked Nov 28 '18 at 17:01
Luca Savant
645
add a comment |
I've encountered this equation:
$$S(t)-y(t)=alpha left(frac{dy(t)}{dt}right)^2$$
where $S(t)$ is a non-defined source (input of our system) and $alpha$ is a positive constant.
I've tried variable separation but without any success.
Please, can someone help me find a solution or a possible approach?
Thanks
differential-equations
edited Nov 30 '18 at 8:03
Dylan
12.4k31026
asked Nov 28 '18 at 17:01
Luca Savant
645
This is equation: $alpha(y’)^2=S-y$?
– player100
Nov 29 '18 at 17:29
Yes! I think that take the derivative of both sides by the variable $t$ produces something similar to the Abel differential equation... But I don't know how to proceed
– Luca Savant
Nov 30 '18 at 22:16
I think that an Abel form is the best you can hope for. Without knowing more about the structure of $S$, it is hard to proceed in generality.
– player100
Dec 2 '18 at 3:30
add a comment |
I've encountered this equation:
$$S(t)-y(t)=alpha left(frac{dy(t)}{dt}right)^2$$
where $S(t)$ is a non-defined source (input of our system) and $alpha$ is a positive constant.
I've tried variable separation but without any success.
Please, can someone help me find a solution or a possible approach?
Thanks
differential-equations
edited Nov 30 '18 at 8:03
Dylan
12.4k31026
asked Nov 28 '18 at 17:01
Luca Savant
645
I've encountered this equation:
$$S(t)-y(t)=alpha left(frac{dy(t)}{dt}right)^2$$
where $S(t)$ is a non-defined source (input of our system) and $alpha$ is a positive constant.
I've tried variable separation but without any success.
Please, can someone help me find a solution or a possible approach?
Thanks
differential-equations
differential-equations
edited Nov 30 '18 at 8:03
Dylan
12.4k31026
asked Nov 28 '18 at 17:01
Luca Savant
645
edited Nov 30 '18 at 8:03
Dylan
12.4k31026
asked Nov 28 '18 at 17:01
Luca Savant
645
edited Nov 30 '18 at 8:03
Dylan
12.4k31026
edited Nov 30 '18 at 8:03
Dylan
12.4k31026
edited Nov 30 '18 at 8:03
Dylan
12.4k31026
12.4k31026
asked Nov 28 '18 at 17:01
Luca Savant
645
asked Nov 28 '18 at 17:01
Luca Savant
645
asked Nov 28 '18 at 17:01
Luca Savant
645
645
This is equation: $alpha(y’)^2=S-y$?
– player100
Nov 29 '18 at 17:29
Yes! I think that take the derivative of both sides by the variable $t$ produces something similar to the Abel differential equation... But I don't know how to proceed
– Luca Savant
Nov 30 '18 at 22:16
I think that an Abel form is the best you can hope for. Without knowing more about the structure of $S$, it is hard to proceed in generality.
– player100
Dec 2 '18 at 3:30
add a comment |
This is equation: $alpha(y’)^2=S-y$?
– player100
Nov 29 '18 at 17:29
Yes! I think that take the derivative of both sides by the variable $t$ produces something similar to the Abel differential equation... But I don't know how to proceed
– Luca Savant
Nov 30 '18 at 22:16
I think that an Abel form is the best you can hope for. Without knowing more about the structure of $S$, it is hard to proceed in generality.
– player100
Dec 2 '18 at 3:30
This is equation: $alpha(y’)^2=S-y$?
– player100
Nov 29 '18 at 17:29
This is equation: $alpha(y’)^2=S-y$?
– player100
Nov 29 '18 at 17:29
Yes! I think that take the derivative of both sides by the variable $t$ produces something similar to the Abel differential equation... But I don't know how to proceed
– Luca Savant
Nov 30 '18 at 22:16
Yes! I think that take the derivative of both sides by the variable $t$ produces something similar to the Abel differential equation... But I don't know how to proceed
– Luca Savant
Nov 30 '18 at 22:16
I think that an Abel form is the best you can hope for. Without knowing more about the structure of $S$, it is hard to proceed in generality.
– player100
Dec 2 '18 at 3:30
I think that an Abel form is the best you can hope for. Without knowing more about the structure of $S$, it is hard to proceed in generality.
– player100
Dec 2 '18 at 3:30
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%2f3017392%2fnonlinear-differential-equation-with-unknown-source%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.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- 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.
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%2f3017392%2fnonlinear-differential-equation-with-unknown-source%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
This is equation: $alpha(y’)^2=S-y$?
– player100
Nov 29 '18 at 17:29
Yes! I think that take the derivative of both sides by the variable $t$ produces something similar to the Abel differential equation... But I don't know how to proceed
– Luca Savant
Nov 30 '18 at 22:16
I think that an Abel form is the best you can hope for. Without knowing more about the structure of $S$, it is hard to proceed in generality.
– player100
Dec 2 '18 at 3:30