Solve $(2xy+e^x) dx + (x^2 y -sin{y}) dy=0$












1












$begingroup$


Solve: $(2xy+e^x) dx + (x^2 y -sin{y}) dy=0$



Clearly, the differential equation is not exact. After applying various methods to no avail, (including power series and Fourier expansion) I cannot see how to get to the solution (an approximating polynomial will do). Online tools are useless here too. Maybe treating it analytically is the only way.



Or does it have a simple solution which I am missing?






real-analysis ordinary-differential-equations approximation







share|cite|improve this question









$endgroup$












  • $begingroup$
    I cannot see one. What could it be?
    $endgroup$
    – Subhasis Biswas
    Jan 29 at 19:05










  • $begingroup$
    Your equation has no solution in the known elementary functions
    $endgroup$
    – Dr. Sonnhard Graubner
    Jan 29 at 19:07










  • $begingroup$
    Then let us try to brute force it
    $endgroup$
    – Subhasis Biswas
    Jan 29 at 19:10
















1












$begingroup$


Solve: $(2xy+e^x) dx + (x^2 y -sin{y}) dy=0$



Clearly, the differential equation is not exact. After applying various methods to no avail, (including power series and Fourier expansion) I cannot see how to get to the solution (an approximating polynomial will do). Online tools are useless here too. Maybe treating it analytically is the only way.



Or does it have a simple solution which I am missing?






real-analysis ordinary-differential-equations approximation







share|cite|improve this question









$endgroup$












  • $begingroup$
    I cannot see one. What could it be?
    $endgroup$
    – Subhasis Biswas
    Jan 29 at 19:05










  • $begingroup$
    Your equation has no solution in the known elementary functions
    $endgroup$
    – Dr. Sonnhard Graubner
    Jan 29 at 19:07










  • $begingroup$
    Then let us try to brute force it
    $endgroup$
    – Subhasis Biswas
    Jan 29 at 19:10














1












1








1


1



$begingroup$


Solve: $(2xy+e^x) dx + (x^2 y -sin{y}) dy=0$



Clearly, the differential equation is not exact. After applying various methods to no avail, (including power series and Fourier expansion) I cannot see how to get to the solution (an approximating polynomial will do). Online tools are useless here too. Maybe treating it analytically is the only way.



Or does it have a simple solution which I am missing?






real-analysis ordinary-differential-equations approximation







share|cite|improve this question









$endgroup$




Solve: $(2xy+e^x) dx + (x^2 y -sin{y}) dy=0$



Clearly, the differential equation is not exact. After applying various methods to no avail, (including power series and Fourier expansion) I cannot see how to get to the solution (an approximating polynomial will do). Online tools are useless here too. Maybe treating it analytically is the only way.



Or does it have a simple solution which I am missing?






real-analysis ordinary-differential-equations approximation




real-analysis ordinary-differential-equations approximation






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Jan 29 at 19:02









Subhasis BiswasSubhasis Biswas

512412




512412












  • $begingroup$
    I cannot see one. What could it be?
    $endgroup$
    – Subhasis Biswas
    Jan 29 at 19:05










  • $begingroup$
    Your equation has no solution in the known elementary functions
    $endgroup$
    – Dr. Sonnhard Graubner
    Jan 29 at 19:07










  • $begingroup$
    Then let us try to brute force it
    $endgroup$
    – Subhasis Biswas
    Jan 29 at 19:10


















  • $begingroup$
    I cannot see one. What could it be?
    $endgroup$
    – Subhasis Biswas
    Jan 29 at 19:05










  • $begingroup$
    Your equation has no solution in the known elementary functions
    $endgroup$
    – Dr. Sonnhard Graubner
    Jan 29 at 19:07










  • $begingroup$
    Then let us try to brute force it
    $endgroup$
    – Subhasis Biswas
    Jan 29 at 19:10
















$begingroup$
I cannot see one. What could it be?
$endgroup$
– Subhasis Biswas
Jan 29 at 19:05




$begingroup$
I cannot see one. What could it be?
$endgroup$
– Subhasis Biswas
Jan 29 at 19:05












$begingroup$
Your equation has no solution in the known elementary functions
$endgroup$
– Dr. Sonnhard Graubner
Jan 29 at 19:07




$begingroup$
Your equation has no solution in the known elementary functions
$endgroup$
– Dr. Sonnhard Graubner
Jan 29 at 19:07












$begingroup$
Then let us try to brute force it
$endgroup$
– Subhasis Biswas
Jan 29 at 19:10




$begingroup$
Then let us try to brute force it
$endgroup$
– Subhasis Biswas
Jan 29 at 19:10










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


















StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3092585%2fsolve-2xyex-dx-x2-y-siny-dy-0%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














StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3092585%2fsolve-2xyex-dx-x2-y-siny-dy-0%23new-answer', 'question_page');
}
);

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







Popular posts from this blog

Can a sorcerer learn a 5th-level spell early by creating spell slots using the Font of Magic feature?

Image
28 6 $begingroup$ Per the Font of Magic feature, sorcerer can use Flexible Casting to create 5th-level spell slots at level 7, even though they are not typically available until level 9. You can transform unexpended sorcery points into one spell slot as a bonus action on your turn. The Creating Spell Slots table shows the cost of creating a spell slot of [5th level is 7] If such a sorcerer levels up while still having this 5th-level spell slot, can they choose a 5th-level spell as the spell they gain upon levelling up? The Spellcasting feature states: Additionally, when you gain a level in this class, you can choose one of the sorcerer spells you know and replace it with another spell from the sorcerer spell list, which also must be of a level for which you have spell slots.
Read more

Does disintegrating a polymorphed enemy still kill it after the 2018 errata?

Image
up vote 13 down vote favorite 1 After the 2018 errata, the disintegrate spell description now reads: A creature targeted by this spell must make a Dexterity saving throw. On a failed save, the target takes 10d6 + 40 force damage. The target is disintegrated if this damage leaves it with 0 hit points. If you were to polymorph an enemy into a rat and then disintegrate it, would the enemy be disintegrated or would it just return to its original form? I know that for Druids, it’s not an instant kill anymore, but is this the case for polymorph as well? dnd-5e spells polymorph errata share | improve this question edited 18 hours ago
Read more

A Topological Invariant for $pi_3(U(n))$

Image
3 3 $begingroup$ Recently, I saw a construction of topological invariant for $pi_3(U(n))$ with $ngeq 2$ : $$ N=frac{1}{24pi^2}int_{S^3} d^3x epsilon^{ijk} Tr[(U^{-1}partial_{x_i}U)(U^{-1}partial_{x_j}U)(U^{-1}partial_{x_k}U)] , $$ where $Uin U(n)$ depends on $boldsymbol{x}=(x_1,x_2,x_3)in S^3$ , $epsilon^{ijk}$ is the Levi-Civita symbol, $i,j,k=1,2,3$ , and the duplicated indexes are summed over. It is claimed that $N$ is an integer, but why? Update 02/02/2019 I think I got an argument for $n=2$ . In this case, $U=e^{i varphi} q$ with $qin SU(2)$ . Due to the trace and the Levi-Civita symbol in $N$ , $varphi$ does not contribute to $N$ . As $Tr[q^{dagger}partial_i q]=0$ and $(q^{dagger}partial_i q)^{dagger}=-q^{dagger}partial_i q$ , $q^{dagger}partial_i q$ in geneeral has the form $q^{dagger}partia
Read more