Frobenius Equation 1: Almost there

  • Thread starter Thread starter Saladsamurai
  • Start date Start date
  • Tags Tags
    Frobenius
Click For Summary
SUMMARY

The discussion focuses on solving the Frobenius equation, specifically the case where the roots of the indicial equation differ by an integer. The user has successfully derived the first solution, y1(x), using the larger root and is now attempting to find the second solution, y2(x), which involves a logarithmic term and a series expansion. The user seeks guidance on determining the coefficients dn and the constant k in the expression for y2(x).

PREREQUISITES
  • Understanding of Frobenius method for solving differential equations
  • Knowledge of indicial equations and their roots
  • Familiarity with series solutions and logarithmic terms in differential equations
  • Basic skills in manipulating algebraic expressions and series summations
NEXT STEPS
  • Research the Frobenius method for finding second solutions to differential equations
  • Study the properties of indicial equations and their implications for solution behavior
  • Learn techniques for determining coefficients in series expansions
  • Explore examples of differential equations with integer-differing roots
USEFUL FOR

Students and researchers in mathematics, particularly those studying differential equations and the Frobenius method, as well as educators looking for examples of solving complex equations.

Saladsamurai
Messages
3,009
Reaction score
7

Homework Statement


Hi :smile: I think I am making some good progress on this one, but I am unsure of what the next step is? Can someone give a nudge in the right direction?

Frobenius1.jpg
 
Physics news on Phys.org
Any thoughts on this one? It is the Frobenius case where the roots of the indicial equation differ by an integer. I have used the larger root to find y1(x) and now I am
seeking y2(x) = k*y1(x)*ln(x) + Σdnxn+s1 where s1 is the smaller root that I found. I have to find the dn's and I also have that 'k' to deal with.
 

Similar threads

Question about the Frobenius method and Bessel functions
  • · Replies 4 ·
Replies
4
Views
3K
Solving differential equation (t^2-1)y''-6y=1
  • · Replies 2 ·
Replies
2
Views
1K
Solve Equation with Method of Frobenius
  • · Replies 4 ·
Replies
4
Views
3K
Method of Frobenius and indicial equations
  • · Replies 4 ·
Replies
4
Views
2K
Proving the Frobenius Norm as a Matrix Norm
  • · Replies 2 ·
Replies
2
Views
4K
Frobenius method for Hermite Equation
  • · Replies 2 ·
Replies
2
Views
6K
Frobenius method and Euler equations
  • · Replies 4 ·
Replies
4
Views
3K
Does limit exist as x approaches zero? Frobenius Method DEQ
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Manifold hypersurface foliation and Frobenius theorem
  • · Replies 73 ·
3
Replies
73
Views
9K
Using the Frobenius Method - 2nd order DE
  • · Replies 1 ·
Replies
1
Views
2K