Whenever $y'$ is in $sin(y')$ or as a power, the degree of the polynomial equation is not defined, why?












0














In my textbook it is written that for $y'+ sinleft(y'right)= 0$ the degree is not defined.
Is it by definition or there is some reasoning behind this?










share|cite|improve this question




















  • 2




    What do you think the degree ought to be? What's the degree of $$2y'-frac16(y')^3+frac1{120}(y')^5-frac1{5040}(y')^7+cdots?$$
    – bof
    Sep 24 '17 at 7:47












  • Ohhhhhhhhh so its not possible to assign a value, then its undefined thanks sooo much
    – WhiteHole
    Sep 24 '17 at 8:05


















0














In my textbook it is written that for $y'+ sinleft(y'right)= 0$ the degree is not defined.
Is it by definition or there is some reasoning behind this?










share|cite|improve this question




















  • 2




    What do you think the degree ought to be? What's the degree of $$2y'-frac16(y')^3+frac1{120}(y')^5-frac1{5040}(y')^7+cdots?$$
    – bof
    Sep 24 '17 at 7:47












  • Ohhhhhhhhh so its not possible to assign a value, then its undefined thanks sooo much
    – WhiteHole
    Sep 24 '17 at 8:05
















0












0








0







In my textbook it is written that for $y'+ sinleft(y'right)= 0$ the degree is not defined.
Is it by definition or there is some reasoning behind this?










share|cite|improve this question















In my textbook it is written that for $y'+ sinleft(y'right)= 0$ the degree is not defined.
Is it by definition or there is some reasoning behind this?







calculus differential-equations






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Nov 29 '18 at 14:46









Davide Giraudo

125k16150261




125k16150261










asked Sep 24 '17 at 5:13









WhiteHoleWhiteHole

216




216








  • 2




    What do you think the degree ought to be? What's the degree of $$2y'-frac16(y')^3+frac1{120}(y')^5-frac1{5040}(y')^7+cdots?$$
    – bof
    Sep 24 '17 at 7:47












  • Ohhhhhhhhh so its not possible to assign a value, then its undefined thanks sooo much
    – WhiteHole
    Sep 24 '17 at 8:05
















  • 2




    What do you think the degree ought to be? What's the degree of $$2y'-frac16(y')^3+frac1{120}(y')^5-frac1{5040}(y')^7+cdots?$$
    – bof
    Sep 24 '17 at 7:47












  • Ohhhhhhhhh so its not possible to assign a value, then its undefined thanks sooo much
    – WhiteHole
    Sep 24 '17 at 8:05










2




2




What do you think the degree ought to be? What's the degree of $$2y'-frac16(y')^3+frac1{120}(y')^5-frac1{5040}(y')^7+cdots?$$
– bof
Sep 24 '17 at 7:47






What do you think the degree ought to be? What's the degree of $$2y'-frac16(y')^3+frac1{120}(y')^5-frac1{5040}(y')^7+cdots?$$
– bof
Sep 24 '17 at 7:47














Ohhhhhhhhh so its not possible to assign a value, then its undefined thanks sooo much
– WhiteHole
Sep 24 '17 at 8:05






Ohhhhhhhhh so its not possible to assign a value, then its undefined thanks sooo much
– WhiteHole
Sep 24 '17 at 8:05












1 Answer
1






active

oldest

votes


















0














begin{array}{l}
y' + sin left( {y'} right) = 0\
{rm{Since, by Maclaurin series expansion of \}}sin left( x right){rm {is}}\
sin left( x right) = x - frac{{{x^3}}}{{3!}} + frac{{{x^5}}}{{5!}} - frac{{{x^7}}}{{7!}} + cdots \
{rm{Then,the first order differential equation can be written as }}\
y' + sin left( {y'} right) = 0\
y' + y' - frac{{{{left( {y'} right)}^3}}}{{3!}} + frac{{{{left( {y'} right)}^5}}}{{5!}} - frac{{{{left( {y'} right)}^7}}}{{7!}} + cdots = 0
end{array}



Then from the above equation, it is clear that there are infinite terms in the equation, so the degree of the equation can not be defined.






share|cite|improve this answer





















    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%2f2442701%2fwhenever-y-is-in-siny-or-as-a-power-the-degree-of-the-polynomial-equat%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









    0














    begin{array}{l}
    y' + sin left( {y'} right) = 0\
    {rm{Since, by Maclaurin series expansion of \}}sin left( x right){rm {is}}\
    sin left( x right) = x - frac{{{x^3}}}{{3!}} + frac{{{x^5}}}{{5!}} - frac{{{x^7}}}{{7!}} + cdots \
    {rm{Then,the first order differential equation can be written as }}\
    y' + sin left( {y'} right) = 0\
    y' + y' - frac{{{{left( {y'} right)}^3}}}{{3!}} + frac{{{{left( {y'} right)}^5}}}{{5!}} - frac{{{{left( {y'} right)}^7}}}{{7!}} + cdots = 0
    end{array}



    Then from the above equation, it is clear that there are infinite terms in the equation, so the degree of the equation can not be defined.






    share|cite|improve this answer


























      0














      begin{array}{l}
      y' + sin left( {y'} right) = 0\
      {rm{Since, by Maclaurin series expansion of \}}sin left( x right){rm {is}}\
      sin left( x right) = x - frac{{{x^3}}}{{3!}} + frac{{{x^5}}}{{5!}} - frac{{{x^7}}}{{7!}} + cdots \
      {rm{Then,the first order differential equation can be written as }}\
      y' + sin left( {y'} right) = 0\
      y' + y' - frac{{{{left( {y'} right)}^3}}}{{3!}} + frac{{{{left( {y'} right)}^5}}}{{5!}} - frac{{{{left( {y'} right)}^7}}}{{7!}} + cdots = 0
      end{array}



      Then from the above equation, it is clear that there are infinite terms in the equation, so the degree of the equation can not be defined.






      share|cite|improve this answer
























        0












        0








        0






        begin{array}{l}
        y' + sin left( {y'} right) = 0\
        {rm{Since, by Maclaurin series expansion of \}}sin left( x right){rm {is}}\
        sin left( x right) = x - frac{{{x^3}}}{{3!}} + frac{{{x^5}}}{{5!}} - frac{{{x^7}}}{{7!}} + cdots \
        {rm{Then,the first order differential equation can be written as }}\
        y' + sin left( {y'} right) = 0\
        y' + y' - frac{{{{left( {y'} right)}^3}}}{{3!}} + frac{{{{left( {y'} right)}^5}}}{{5!}} - frac{{{{left( {y'} right)}^7}}}{{7!}} + cdots = 0
        end{array}



        Then from the above equation, it is clear that there are infinite terms in the equation, so the degree of the equation can not be defined.






        share|cite|improve this answer












        begin{array}{l}
        y' + sin left( {y'} right) = 0\
        {rm{Since, by Maclaurin series expansion of \}}sin left( x right){rm {is}}\
        sin left( x right) = x - frac{{{x^3}}}{{3!}} + frac{{{x^5}}}{{5!}} - frac{{{x^7}}}{{7!}} + cdots \
        {rm{Then,the first order differential equation can be written as }}\
        y' + sin left( {y'} right) = 0\
        y' + y' - frac{{{{left( {y'} right)}^3}}}{{3!}} + frac{{{{left( {y'} right)}^5}}}{{5!}} - frac{{{{left( {y'} right)}^7}}}{{7!}} + cdots = 0
        end{array}



        Then from the above equation, it is clear that there are infinite terms in the equation, so the degree of the equation can not be defined.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Nov 29 '18 at 17:08









        Krishna SrivastavKrishna Srivastav

        894




        894






























            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.





            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.




            draft saved


            draft discarded














            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2442701%2fwhenever-y-is-in-siny-or-as-a-power-the-degree-of-the-polynomial-equat%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

            Ellipse (mathématiques)

            Quarter-circle Tiles

            Mont Emei