Solving a non-linear differential equation of second degree
How do I solve the differential equation $y^2= 2px+ p^2 $, $ $ $p$ $ $ being $frac{dy}{dx}$? I came up with this equation accidentally while trying to copy an exercise from the book. The actual problem is fine, but this equation is troubling me for a while. I tried reducing it to Clairaut's form to no avail. I tried solving for $y$ or $x$, but failed. Kindly help me out.
differential-equations derivatives
asked Nov 22 '18 at 17:19
Subhasis BiswasSubhasis Biswas
441211
|
show 3 more comments
How do I solve the differential equation $y^2= 2px+ p^2 $, $ $ $p$ $ $ being $frac{dy}{dx}$? I came up with this equation accidentally while trying to copy an exercise from the book. The actual problem is fine, but this equation is troubling me for a while. I tried reducing it to Clairaut's form to no avail. I tried solving for $y$ or $x$, but failed. Kindly help me out.
differential-equations derivatives
asked Nov 22 '18 at 17:19
Subhasis BiswasSubhasis Biswas
441211
1
You can solve for $p$ as $$p = dfrac{dy}{dx} = -x~pm~ sqrt{x^2+y^2}$$ However, I am not sure you can solve the resulting differential equation.
– Moo
Nov 22 '18 at 17:31
I am totally lost from here. No idea. In fact, I tried fiddling around this format before.
– Subhasis Biswas
Nov 22 '18 at 17:33
You would to resort to numerical methods at this point.
– Moo
Nov 22 '18 at 17:33
1
@Isham: Oops - just a typo - corrected - thanks.
– Moo
Nov 22 '18 at 17:36
1
@Isham It should be a $-$
– Subhasis Biswas
Nov 22 '18 at 17:36
|
show 3 more comments
How do I solve the differential equation $y^2= 2px+ p^2 $, $ $ $p$ $ $ being $frac{dy}{dx}$? I came up with this equation accidentally while trying to copy an exercise from the book. The actual problem is fine, but this equation is troubling me for a while. I tried reducing it to Clairaut's form to no avail. I tried solving for $y$ or $x$, but failed. Kindly help me out.
differential-equations derivatives
asked Nov 22 '18 at 17:19
Subhasis BiswasSubhasis Biswas
441211
How do I solve the differential equation $y^2= 2px+ p^2 $, $ $ $p$ $ $ being $frac{dy}{dx}$? I came up with this equation accidentally while trying to copy an exercise from the book. The actual problem is fine, but this equation is troubling me for a while. I tried reducing it to Clairaut's form to no avail. I tried solving for $y$ or $x$, but failed. Kindly help me out.
differential-equations derivatives
differential-equations derivatives
asked Nov 22 '18 at 17:19
Subhasis BiswasSubhasis Biswas
441211
asked Nov 22 '18 at 17:19
Subhasis BiswasSubhasis Biswas
441211
edited Nov 22 '18 at 17:27
Subhasis Biswas
asked Nov 22 '18 at 17:19
Subhasis BiswasSubhasis Biswas
441211
asked Nov 22 '18 at 17:19
Subhasis BiswasSubhasis Biswas
441211
asked Nov 22 '18 at 17:19
Subhasis BiswasSubhasis Biswas
441211
441211
1
You can solve for $p$ as $$p = dfrac{dy}{dx} = -x~pm~ sqrt{x^2+y^2}$$ However, I am not sure you can solve the resulting differential equation.
– Moo
Nov 22 '18 at 17:31
I am totally lost from here. No idea. In fact, I tried fiddling around this format before.
– Subhasis Biswas
Nov 22 '18 at 17:33
You would to resort to numerical methods at this point.
– Moo
Nov 22 '18 at 17:33
1
@Isham: Oops - just a typo - corrected - thanks.
– Moo
Nov 22 '18 at 17:36
1
@Isham It should be a $-$
– Subhasis Biswas
Nov 22 '18 at 17:36
|
show 3 more comments
1
You can solve for $p$ as $$p = dfrac{dy}{dx} = -x~pm~ sqrt{x^2+y^2}$$ However, I am not sure you can solve the resulting differential equation.
– Moo
Nov 22 '18 at 17:31
I am totally lost from here. No idea. In fact, I tried fiddling around this format before.
– Subhasis Biswas
Nov 22 '18 at 17:33
You would to resort to numerical methods at this point.
– Moo
Nov 22 '18 at 17:33
1
@Isham: Oops - just a typo - corrected - thanks.
– Moo
Nov 22 '18 at 17:36
1
@Isham It should be a $-$
– Subhasis Biswas
Nov 22 '18 at 17:36
1
1
You can solve for $p$ as $$p = dfrac{dy}{dx} = -x~pm~ sqrt{x^2+y^2}$$ However, I am not sure you can solve the resulting differential equation.
– Moo
Nov 22 '18 at 17:31
You can solve for $p$ as $$p = dfrac{dy}{dx} = -x~pm~ sqrt{x^2+y^2}$$ However, I am not sure you can solve the resulting differential equation.
– Moo
Nov 22 '18 at 17:31
I am totally lost from here. No idea. In fact, I tried fiddling around this format before.
– Subhasis Biswas
Nov 22 '18 at 17:33
I am totally lost from here. No idea. In fact, I tried fiddling around this format before.
– Subhasis Biswas
Nov 22 '18 at 17:33
You would to resort to numerical methods at this point.
– Moo
Nov 22 '18 at 17:33
You would to resort to numerical methods at this point.
– Moo
Nov 22 '18 at 17:33
1
1
@Isham: Oops - just a typo - corrected - thanks.
– Moo
Nov 22 '18 at 17:36
@Isham: Oops - just a typo - corrected - thanks.
– Moo
Nov 22 '18 at 17:36
1
1
@Isham It should be a $-$
– Subhasis Biswas
Nov 22 '18 at 17:36
@Isham It should be a $-$
– Subhasis Biswas
Nov 22 '18 at 17:36
|
show 3 more comments
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%2f3009377%2fsolving-a-non-linear-differential-equation-of-second-degree%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%2f3009377%2fsolving-a-non-linear-differential-equation-of-second-degree%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
You can solve for $p$ as $$p = dfrac{dy}{dx} = -x~pm~ sqrt{x^2+y^2}$$ However, I am not sure you can solve the resulting differential equation.
– Moo
Nov 22 '18 at 17:31
I am totally lost from here. No idea. In fact, I tried fiddling around this format before.
– Subhasis Biswas
Nov 22 '18 at 17:33
You would to resort to numerical methods at this point.
– Moo
Nov 22 '18 at 17:33
1
@Isham: Oops - just a typo - corrected - thanks.
– Moo
Nov 22 '18 at 17:36
1
@Isham It should be a $-$
– Subhasis Biswas
Nov 22 '18 at 17:36