Why can’t we apply Method of separation of variables to second order Diff equations?

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
5
down vote

favorite












Suppose we are solving the following ODE $$mathrmdyover mathrmdx=yover x$$ then we can solve it by seperation of variables method. But if we have to solve $$mathrmd^2yover mathrmdx^2 = yover x$$ then why cant we seperate $mathrmd^2yover mathrmdx^2$?







share|cite|improve this question






















  • Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
    – José Carlos Santos
    Aug 20 at 11:32














up vote
5
down vote

favorite












Suppose we are solving the following ODE $$mathrmdyover mathrmdx=yover x$$ then we can solve it by seperation of variables method. But if we have to solve $$mathrmd^2yover mathrmdx^2 = yover x$$ then why cant we seperate $mathrmd^2yover mathrmdx^2$?







share|cite|improve this question






















  • Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
    – José Carlos Santos
    Aug 20 at 11:32












up vote
5
down vote

favorite









up vote
5
down vote

favorite











Suppose we are solving the following ODE $$mathrmdyover mathrmdx=yover x$$ then we can solve it by seperation of variables method. But if we have to solve $$mathrmd^2yover mathrmdx^2 = yover x$$ then why cant we seperate $mathrmd^2yover mathrmdx^2$?







share|cite|improve this question














Suppose we are solving the following ODE $$mathrmdyover mathrmdx=yover x$$ then we can solve it by seperation of variables method. But if we have to solve $$mathrmd^2yover mathrmdx^2 = yover x$$ then why cant we seperate $mathrmd^2yover mathrmdx^2$?









share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 20 at 11:44









Bernard

111k635103




111k635103










asked Aug 20 at 11:29









megha gill

261




261











  • Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
    – José Carlos Santos
    Aug 20 at 11:32
















  • Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
    – José Carlos Santos
    Aug 20 at 11:32















Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Aug 20 at 11:32




Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Aug 20 at 11:32










2 Answers
2






active

oldest

votes

















up vote
4
down vote













You have to be cautious: remember that $$fracd^2ydx^2 = fracdleft(fracdydxright)dx$$ So you could use separation of variables, but your ODE will become $$frac1ydleft(fracdydxright) = frac1xdx$$ and not $$frac1ydydy = frac1xdxdx;;;;colorredtextWrong$$






share|cite|improve this answer



























    up vote
    0
    down vote













    Because you can't write $$dfracd^2 yy=dfracdx^2x$$or equivalently $$dfracd^2yy=dfracdx cdot dxx$$this is meaningless. Also you would be stopped in the next step. $int dfracd^2yy$ and $intdfracdx^2x$ are both illegal.






    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',
      convertImagesToLinks: true,
      noModals: false,
      showLowRepImageUploadWarning: true,
      reputationToPostImages: 10,
      bindNavPrevention: true,
      postfix: "",
      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%2f2888664%2fwhy-can-t-we-apply-method-of-separation-of-variables-to-second-order-diff-equati%23new-answer', 'question_page');

      );

      Post as a guest






























      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes








      up vote
      4
      down vote













      You have to be cautious: remember that $$fracd^2ydx^2 = fracdleft(fracdydxright)dx$$ So you could use separation of variables, but your ODE will become $$frac1ydleft(fracdydxright) = frac1xdx$$ and not $$frac1ydydy = frac1xdxdx;;;;colorredtextWrong$$






      share|cite|improve this answer
























        up vote
        4
        down vote













        You have to be cautious: remember that $$fracd^2ydx^2 = fracdleft(fracdydxright)dx$$ So you could use separation of variables, but your ODE will become $$frac1ydleft(fracdydxright) = frac1xdx$$ and not $$frac1ydydy = frac1xdxdx;;;;colorredtextWrong$$






        share|cite|improve this answer






















          up vote
          4
          down vote










          up vote
          4
          down vote









          You have to be cautious: remember that $$fracd^2ydx^2 = fracdleft(fracdydxright)dx$$ So you could use separation of variables, but your ODE will become $$frac1ydleft(fracdydxright) = frac1xdx$$ and not $$frac1ydydy = frac1xdxdx;;;;colorredtextWrong$$






          share|cite|improve this answer












          You have to be cautious: remember that $$fracd^2ydx^2 = fracdleft(fracdydxright)dx$$ So you could use separation of variables, but your ODE will become $$frac1ydleft(fracdydxright) = frac1xdx$$ and not $$frac1ydydy = frac1xdxdx;;;;colorredtextWrong$$







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Aug 20 at 11:42









          Davide Morgante

          2,343422




          2,343422




















              up vote
              0
              down vote













              Because you can't write $$dfracd^2 yy=dfracdx^2x$$or equivalently $$dfracd^2yy=dfracdx cdot dxx$$this is meaningless. Also you would be stopped in the next step. $int dfracd^2yy$ and $intdfracdx^2x$ are both illegal.






              share|cite|improve this answer
























                up vote
                0
                down vote













                Because you can't write $$dfracd^2 yy=dfracdx^2x$$or equivalently $$dfracd^2yy=dfracdx cdot dxx$$this is meaningless. Also you would be stopped in the next step. $int dfracd^2yy$ and $intdfracdx^2x$ are both illegal.






                share|cite|improve this answer






















                  up vote
                  0
                  down vote










                  up vote
                  0
                  down vote









                  Because you can't write $$dfracd^2 yy=dfracdx^2x$$or equivalently $$dfracd^2yy=dfracdx cdot dxx$$this is meaningless. Also you would be stopped in the next step. $int dfracd^2yy$ and $intdfracdx^2x$ are both illegal.






                  share|cite|improve this answer












                  Because you can't write $$dfracd^2 yy=dfracdx^2x$$or equivalently $$dfracd^2yy=dfracdx cdot dxx$$this is meaningless. Also you would be stopped in the next step. $int dfracd^2yy$ and $intdfracdx^2x$ are both illegal.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Aug 20 at 11:44









                  Mostafa Ayaz

                  9,7483730




                  9,7483730






















                       

                      draft saved


                      draft discarded


























                       


                      draft saved


                      draft discarded














                      StackExchange.ready(
                      function ()
                      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2888664%2fwhy-can-t-we-apply-method-of-separation-of-variables-to-second-order-diff-equati%23new-answer', 'question_page');

                      );

                      Post as a guest













































































                      這個網誌中的熱門文章

                      How to combine Bézier curves to a surface?

                      Carbon dioxide

                      Why am i infinitely getting the same tweet with the Twitter Search API?