Second order ODE, separation of variables ??
0
$begingroup$
I have an ODE of the form:
$frac{d^2y}{dx^2}=frac{f(y)}{g(x)}$
I understand how to separate variables and integrate if its first order, but it looks trickier if its second order, is there a general way to solve it ?
differential
asked Dec 23 '18 at 18:40
ODEODE
141
$endgroup$
add a comment |
0
$begingroup$
I have an ODE of the form:
$frac{d^2y}{dx^2}=frac{f(y)}{g(x)}$
I understand how to separate variables and integrate if its first order, but it looks trickier if its second order, is there a general way to solve it ?
differential
asked Dec 23 '18 at 18:40
ODEODE
141
$endgroup$
1
$begingroup$
$frac{d^2y}{dx^2}=frac{dy'}{dx}$, so if you have a function of $y'$ instead of $y$ on the $RHS$, you can solve using separation of variables
$endgroup$
– Shubham Johri
Dec 23 '18 at 18:44
$begingroup$
Yeah I know that, doesn't solve the problem and not the question I asked, but thank you anyway
$endgroup$
– ODE
Dec 23 '18 at 18:55
$begingroup$
Are you asking about how to solve $2^{nd}$ order $ODE$s using separation of variables or otherwise?
$endgroup$
– Shubham Johri
Dec 23 '18 at 18:58
$begingroup$
I'm asking how to solve a second order ODE of that form, where we can separate the variables into two independent functions,
$endgroup$
– ODE
Dec 23 '18 at 19:03
add a comment |
0
0
0
0
$begingroup$
I have an ODE of the form:
$frac{d^2y}{dx^2}=frac{f(y)}{g(x)}$
I understand how to separate variables and integrate if its first order, but it looks trickier if its second order, is there a general way to solve it ?
differential
asked Dec 23 '18 at 18:40
ODEODE
141
$endgroup$
I have an ODE of the form:
$frac{d^2y}{dx^2}=frac{f(y)}{g(x)}$
I understand how to separate variables and integrate if its first order, but it looks trickier if its second order, is there a general way to solve it ?
differential
differential
asked Dec 23 '18 at 18:40
ODEODE
141
asked Dec 23 '18 at 18:40
ODEODE
141
asked Dec 23 '18 at 18:40
ODEODE
141
asked Dec 23 '18 at 18:40
ODEODE
141
asked Dec 23 '18 at 18:40
ODEODE
141
141
1
$begingroup$
$frac{d^2y}{dx^2}=frac{dy'}{dx}$, so if you have a function of $y'$ instead of $y$ on the $RHS$, you can solve using separation of variables
$endgroup$
– Shubham Johri
Dec 23 '18 at 18:44
$begingroup$
Yeah I know that, doesn't solve the problem and not the question I asked, but thank you anyway
$endgroup$
– ODE
Dec 23 '18 at 18:55
$begingroup$
Are you asking about how to solve $2^{nd}$ order $ODE$s using separation of variables or otherwise?
$endgroup$
– Shubham Johri
Dec 23 '18 at 18:58
$begingroup$
I'm asking how to solve a second order ODE of that form, where we can separate the variables into two independent functions,
$endgroup$
– ODE
Dec 23 '18 at 19:03
add a comment |
1
$begingroup$
$frac{d^2y}{dx^2}=frac{dy'}{dx}$, so if you have a function of $y'$ instead of $y$ on the $RHS$, you can solve using separation of variables
$endgroup$
– Shubham Johri
Dec 23 '18 at 18:44
$begingroup$
Yeah I know that, doesn't solve the problem and not the question I asked, but thank you anyway
$endgroup$
– ODE
Dec 23 '18 at 18:55
$begingroup$
Are you asking about how to solve $2^{nd}$ order $ODE$s using separation of variables or otherwise?
$endgroup$
– Shubham Johri
Dec 23 '18 at 18:58
$begingroup$
I'm asking how to solve a second order ODE of that form, where we can separate the variables into two independent functions,
$endgroup$
– ODE
Dec 23 '18 at 19:03
1
1
$begingroup$
$frac{d^2y}{dx^2}=frac{dy'}{dx}$, so if you have a function of $y'$ instead of $y$ on the $RHS$, you can solve using separation of variables
$endgroup$
– Shubham Johri
Dec 23 '18 at 18:44
$begingroup$
$frac{d^2y}{dx^2}=frac{dy'}{dx}$, so if you have a function of $y'$ instead of $y$ on the $RHS$, you can solve using separation of variables
$endgroup$
– Shubham Johri
Dec 23 '18 at 18:44
$begingroup$
Yeah I know that, doesn't solve the problem and not the question I asked, but thank you anyway
$endgroup$
– ODE
Dec 23 '18 at 18:55
$begingroup$
Yeah I know that, doesn't solve the problem and not the question I asked, but thank you anyway
$endgroup$
– ODE
Dec 23 '18 at 18:55
$begingroup$
Are you asking about how to solve $2^{nd}$ order $ODE$s using separation of variables or otherwise?
$endgroup$
– Shubham Johri
Dec 23 '18 at 18:58
$begingroup$
Are you asking about how to solve $2^{nd}$ order $ODE$s using separation of variables or otherwise?
$endgroup$
– Shubham Johri
Dec 23 '18 at 18:58
$begingroup$
I'm asking how to solve a second order ODE of that form, where we can separate the variables into two independent functions,
$endgroup$
– ODE
Dec 23 '18 at 19:03
$begingroup$
I'm asking how to solve a second order ODE of that form, where we can separate the variables into two independent functions,
$endgroup$
– ODE
Dec 23 '18 at 19:03
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%2f3050598%2fsecond-order-ode-separation-of-variables%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%2f3050598%2fsecond-order-ode-separation-of-variables%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
1
$begingroup$
$frac{d^2y}{dx^2}=frac{dy'}{dx}$, so if you have a function of $y'$ instead of $y$ on the $RHS$, you can solve using separation of variables
$endgroup$
– Shubham Johri
Dec 23 '18 at 18:44
$begingroup$
Yeah I know that, doesn't solve the problem and not the question I asked, but thank you anyway
$endgroup$
– ODE
Dec 23 '18 at 18:55
$begingroup$
Are you asking about how to solve $2^{nd}$ order $ODE$s using separation of variables or otherwise?
$endgroup$
– Shubham Johri
Dec 23 '18 at 18:58
$begingroup$
I'm asking how to solve a second order ODE of that form, where we can separate the variables into two independent functions,
$endgroup$
– ODE
Dec 23 '18 at 19:03