When using the Frobenius method, and r1-r2 is neither zero nor a positive integer, can you use the Wronskian to find the second solution?When solving an ODE using power series method, Why do we need to expand the solution around the singular point?Frobenius method, why is it an issue when the roots of the indicial equation differ by an integerCan I solve an Euler differential equation by using the Frobenius method?A different method for solving 2nd order ODEsI'm having trouble using the Frobenius Method to solve $x^2 fracd^2 ydx^2-2x fracdydx+2y=0$Finding the second linearly independent solution, given the first, using the method of FrobeniusCan one use the Wronskian to find both solutions of a 2nd order homogenous DE?when are the successive approximations using picard's method for solving an ODE, are the terms of the taylor expansion of the solution of the ODEFind the second order differential equation with given the solution and appropriate initial conditionsBessel equation of zero order of second kind using the frobenius method.

Can we compute the area of a quadrilateral with one right angle when we only know the lengths of any three sides?

All in one piece, we mend holes in your socks

How to tell a function to use the default argument values?

Why didn't Boeing produce its own regional jet?

How dangerous is XSS?

What mechanic is there to disable a threat instead of killing it?

How do I handle a potential work/personal life conflict as the manager of one of my friends?

Is it inappropriate for a student to attend their mentor's dissertation defense?

Is it acceptable for a professor to tell male students to not think that they are smarter than female students?

I would say: "You are another teacher", but she is a woman and I am a man

How to prevent "they're falling in love" trope

How does a predictive coding aid in lossless compression?

Can a virus destroy the BIOS of a modern computer?

Is it logically or scientifically possible to artificially send energy to the body?

How to show a landlord what we have in savings?

Plagiarism or not?

How can I deal with my CEO asking me to hire someone with a higher salary than me, a co-founder?

Bullying boss launched a smear campaign and made me unemployable

How badly should I try to prevent a user from XSSing themselves?

Is there an expression that means doing something right before you will need it rather than doing it in case you might need it?

Are there any examples of a variable being normally distributed that is *not* due to the Central Limit Theorem?

Should I tell management that I intend to leave due to bad software development practices?

How to Recreate this in LaTeX? (Unsure What the Notation is Called)

Why is consensus so controversial in Britain?



When using the Frobenius method, and r1-r2 is neither zero nor a positive integer, can you use the Wronskian to find the second solution?


When solving an ODE using power series method, Why do we need to expand the solution around the singular point?Frobenius method, why is it an issue when the roots of the indicial equation differ by an integerCan I solve an Euler differential equation by using the Frobenius method?A different method for solving 2nd order ODEsI'm having trouble using the Frobenius Method to solve $x^2 fracd^2 ydx^2-2x fracdydx+2y=0$Finding the second linearly independent solution, given the first, using the method of FrobeniusCan one use the Wronskian to find both solutions of a 2nd order homogenous DE?when are the successive approximations using picard's method for solving an ODE, are the terms of the taylor expansion of the solution of the ODEFind the second order differential equation with given the solution and appropriate initial conditionsBessel equation of zero order of second kind using the frobenius method.













1












$begingroup$


When using the Frobenius method, and r1-r2 is neither zero nor a positive integer, can you use the Wronskian to find the second solution? Basically, do I have to repeat the substitution with the second root in order to find the second solution to an ODE or is there an easier way with the Wronskian?










share|cite|improve this question









$endgroup$
















    1












    $begingroup$


    When using the Frobenius method, and r1-r2 is neither zero nor a positive integer, can you use the Wronskian to find the second solution? Basically, do I have to repeat the substitution with the second root in order to find the second solution to an ODE or is there an easier way with the Wronskian?










    share|cite|improve this question









    $endgroup$














      1












      1








      1


      1



      $begingroup$


      When using the Frobenius method, and r1-r2 is neither zero nor a positive integer, can you use the Wronskian to find the second solution? Basically, do I have to repeat the substitution with the second root in order to find the second solution to an ODE or is there an easier way with the Wronskian?










      share|cite|improve this question









      $endgroup$




      When using the Frobenius method, and r1-r2 is neither zero nor a positive integer, can you use the Wronskian to find the second solution? Basically, do I have to repeat the substitution with the second root in order to find the second solution to an ODE or is there an easier way with the Wronskian?







      ordinary-differential-equations frobenius-method






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Mar 28 at 20:58









      Fernando VarelaFernando Varela

      253




      253




















          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%2f3166413%2fwhen-using-the-frobenius-method-and-r1-r2-is-neither-zero-nor-a-positive-intege%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%2f3166413%2fwhen-using-the-frobenius-method-and-r1-r2-is-neither-zero-nor-a-positive-intege%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

          Triangular numbers and gcdProving sum of a set is $0 pmod n$ if $n$ is odd, or $fracn2 pmod n$ if $n$ is even?Is greatest common divisor of two numbers really their smallest linear combination?GCD, LCM RelationshipProve a set of nonnegative integers with greatest common divisor 1 and closed under addition has all but finite many nonnegative integers.all pairs of a and b in an equation containing gcdTriangular Numbers Modulo $k$ - Hit All Values?Understanding the Existence and Uniqueness of the GCDGCD and LCM with logical symbolsThe greatest common divisor of two positive integers less than 100 is equal to 3. Their least common multiple is twelve times one of the integers.Suppose that for all integers $x$, $x|a$ and $x|b$ if and only if $x|c$. Then $c = gcd(a,b)$Which is the gcd of 2 numbers which are multiplied and the result is 600000?

          Ingelân Ynhâld Etymology | Geografy | Skiednis | Polityk en bestjoer | Ekonomy | Demografy | Kultuer | Klimaat | Sjoch ek | Keppelings om utens | Boarnen, noaten en referinsjes Navigaasjemenuwww.gov.ukOffisjele webside fan it regear fan it Feriene KeninkrykOffisjele webside fan it Britske FerkearsburoNederlânsktalige ynformaasje fan it Britske FerkearsburoOffisjele webside fan English Heritage, de organisaasje dy't him ynset foar it behâld fan it Ingelske kultuergoedYnwennertallen fan alle Britske stêden út 'e folkstelling fan 2011Notes en References, op dizze sideEngland

          Հադիս Բովանդակություն Անվանում և նշանակություն | Դասակարգում | Աղբյուրներ | Նավարկման ցանկ