How to solve a differential equation with a term to a power? The Next CEO of Stack OverflowHow do I solve this differential equation?Solving differential equation $x^2y''-xy'+y=0, x>0$ with non-constant coefficients using characteristic equation?Solution to differential equationCan I solve an Euler differential equation by using the Frobenius method?How to solve a differential equationHelp needed with differential equationHow to solve differential equations that look like theseHow to solve differential equation with one differential termsolve differential equation $fracdPdt = kPcos^2(rt-Theta)$How to solve an exponential differential equation?
What connection does MS Office have to Netscape Navigator?
Received an invoice from my ex-employer billing me for training; how to handle?
Is there a difference between "Fahrstuhl" and "Aufzug"
FBX seems to be empty when imported into Blender
How fast would a person need to move to trick the eye?
Does it take more energy to get to Venus or to Mars?
What benefits would be gained by using human laborers instead of drones in deep sea mining?
What is the result of assigning to std::vector<T>::begin()?
Giving the same color to different shapefiles in QGIS
Non-deterministic sum of floats
Unreliable Magic - Is it worth it?
If the heap is initialized for security, then why is the stack uninitialized?
What does convergence in distribution "in the Gromov–Hausdorff" sense mean?
Complex fractions
How to transpose the 1st and -1th levels of arbitrarily nested array?
How do scammers retract money, while you can’t?
At which OSI layer a user-generated data resides?
A "random" question: usage of "random" as adjective in Spanish
What does "Its cash flow is deeply negative" mean?
Is it possible to search for a directory/file combination?
What is ( CFMCC ) on ILS approach chart?
What exact does MIB represent in SNMP? How is it different from OID?
Extending anchors in TikZ
Elegant way to replace substring in a regex with optional groups in Python?
How to solve a differential equation with a term to a power?
The Next CEO of Stack OverflowHow do I solve this differential equation?Solving differential equation $x^2y''-xy'+y=0, x>0$ with non-constant coefficients using characteristic equation?Solution to differential equationCan I solve an Euler differential equation by using the Frobenius method?How to solve a differential equationHelp needed with differential equationHow to solve differential equations that look like theseHow to solve differential equation with one differential termsolve differential equation $fracdPdt = kPcos^2(rt-Theta)$How to solve an exponential differential equation?
$begingroup$
How would I solve an equation where one of the differential terms is to a power? For example:
$fracd^2ydx^2+k(fracdydx)^2=0$?
I've been given advice to use the $D$ operator which apparently means $fracddx()$ but I'm not sure how that's applicable to this scenario. Any alternative suggestions or explanations would be appreciated!
calculus ordinary-differential-equations
asked 4 hours ago
Ammar TarajiaAmmar Tarajia
111
New contributor
Ammar Tarajia is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
How would I solve an equation where one of the differential terms is to a power? For example:
$fracd^2ydx^2+k(fracdydx)^2=0$?
I've been given advice to use the $D$ operator which apparently means $fracddx()$ but I'm not sure how that's applicable to this scenario. Any alternative suggestions or explanations would be appreciated!
calculus ordinary-differential-equations
asked 4 hours ago
Ammar TarajiaAmmar Tarajia
111
New contributor
Ammar Tarajia is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
How would I solve an equation where one of the differential terms is to a power? For example:
$fracd^2ydx^2+k(fracdydx)^2=0$?
I've been given advice to use the $D$ operator which apparently means $fracddx()$ but I'm not sure how that's applicable to this scenario. Any alternative suggestions or explanations would be appreciated!
calculus ordinary-differential-equations
asked 4 hours ago
Ammar TarajiaAmmar Tarajia
111
New contributor
Ammar Tarajia is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
How would I solve an equation where one of the differential terms is to a power? For example:
$fracd^2ydx^2+k(fracdydx)^2=0$?
I've been given advice to use the $D$ operator which apparently means $fracddx()$ but I'm not sure how that's applicable to this scenario. Any alternative suggestions or explanations would be appreciated!
calculus ordinary-differential-equations
calculus ordinary-differential-equations
asked 4 hours ago
Ammar TarajiaAmmar Tarajia
111
New contributor
Ammar Tarajia is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 4 hours ago
Ammar TarajiaAmmar Tarajia
111
New contributor
Ammar Tarajia is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 4 hours ago
Ammar TarajiaAmmar Tarajia
111
New contributor
Ammar Tarajia is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 4 hours ago
Ammar TarajiaAmmar Tarajia
111
asked 4 hours ago
Ammar TarajiaAmmar Tarajia
111
111
New contributor
Ammar Tarajia is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Ammar Tarajia is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Ammar Tarajia is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Since you only have second and first derivatives of $y$ and no
un-differentiated $y$, you could try to introduce the new function $v=fracdydx$. Your differential equation will turn into $fracdvdx+kv^2=0$, and I guess you will manage to take it from here.
answered 4 hours ago
mickepmickep
18.7k12250
$endgroup$
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
);
);
Ammar Tarajia is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
var $window = $(window),
onScroll = function(e)
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom))
StackExchange.using('gps', function() StackExchange.gps.track('embedded_signup_form.view', location: 'question_page' ); );
$window.unbind('scroll', onScroll);
;
$window.on('scroll', onScroll);
);
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%2f3167430%2fhow-to-solve-a-differential-equation-with-a-term-to-a-power%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
$begingroup$
Since you only have second and first derivatives of $y$ and no
un-differentiated $y$, you could try to introduce the new function $v=fracdydx$. Your differential equation will turn into $fracdvdx+kv^2=0$, and I guess you will manage to take it from here.
answered 4 hours ago
mickepmickep
18.7k12250
$endgroup$
add a comment |
$begingroup$
Since you only have second and first derivatives of $y$ and no
un-differentiated $y$, you could try to introduce the new function $v=fracdydx$. Your differential equation will turn into $fracdvdx+kv^2=0$, and I guess you will manage to take it from here.
answered 4 hours ago
mickepmickep
18.7k12250
$endgroup$
add a comment |
$begingroup$
Since you only have second and first derivatives of $y$ and no
un-differentiated $y$, you could try to introduce the new function $v=fracdydx$. Your differential equation will turn into $fracdvdx+kv^2=0$, and I guess you will manage to take it from here.
answered 4 hours ago
mickepmickep
18.7k12250
$endgroup$
Since you only have second and first derivatives of $y$ and no
un-differentiated $y$, you could try to introduce the new function $v=fracdydx$. Your differential equation will turn into $fracdvdx+kv^2=0$, and I guess you will manage to take it from here.
answered 4 hours ago
mickepmickep
18.7k12250
answered 4 hours ago
mickepmickep
18.7k12250
answered 4 hours ago
mickepmickep
18.7k12250
answered 4 hours ago
mickepmickep
18.7k12250
18.7k12250
add a comment |
add a comment |
Ammar Tarajia is a new contributor. Be nice, and check out our Code of Conduct.
Ammar Tarajia is a new contributor. Be nice, and check out our Code of Conduct.
Ammar Tarajia is a new contributor. Be nice, and check out our Code of Conduct.
Ammar Tarajia is a new contributor. Be nice, and check out our Code of Conduct.
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');
var $window = $(window),
onScroll = function(e)
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom))
StackExchange.using('gps', function() StackExchange.gps.track('embedded_signup_form.view', location: 'question_page' ); );
$window.unbind('scroll', onScroll);
;
$window.on('scroll', onScroll);
);
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%2f3167430%2fhow-to-solve-a-differential-equation-with-a-term-to-a-power%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');
var $window = $(window),
onScroll = function(e)
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom))
StackExchange.using('gps', function() StackExchange.gps.track('embedded_signup_form.view', location: 'question_page' ); );
$window.unbind('scroll', onScroll);
;
$window.on('scroll', onScroll);
);
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');
var $window = $(window),
onScroll = function(e)
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom))
StackExchange.using('gps', function() StackExchange.gps.track('embedded_signup_form.view', location: 'question_page' ); );
$window.unbind('scroll', onScroll);
;
$window.on('scroll', onScroll);
);
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');
var $window = $(window),
onScroll = function(e)
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom))
StackExchange.using('gps', function() StackExchange.gps.track('embedded_signup_form.view', location: 'question_page' ); );
$window.unbind('scroll', onScroll);
;
$window.on('scroll', onScroll);
);
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
