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Saladsamurai
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Homework Statement
Hi
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? Frobenius Equation 1: Almost there
- Thread starter Saladsamurai
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In summary, the conversation is about finding the second solution for the Frobenius case where the roots of the indicial equation differ by an integer. The person is seeking help in finding y2(x) which involves finding the dn's and dealing with the variable 'k'.
Hi
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? - #2
Saladsamurai
- 3,020
- 7
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.
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.
Related to Frobenius Equation 1: Almost there
1. What is the Frobenius Equation 1?
The Frobenius Equation 1 is a mathematical equation developed by German mathematician Ferdinand Georg Frobenius. It is used to find the solutions to certain types of differential equations and has applications in various fields of science and engineering.
2. How is the Frobenius Equation 1 different from other differential equations?
The Frobenius Equation 1 is different from other differential equations because it involves a singular point, which is a point where the equation becomes undefined. This makes it more challenging to solve compared to regular differential equations.
3. What is the importance of the Frobenius Equation 1 in science?
The Frobenius Equation 1 has many applications in science, particularly in physics and engineering. It is used to find solutions to problems involving waves, heat transfer, and quantum mechanics. It is also used in the study of fluid dynamics and electromagnetics.
4. Can the Frobenius Equation 1 be solved analytically?
Yes, the Frobenius Equation 1 can be solved analytically. However, the solutions can be complex and involve infinite series. In some cases, the equation may not have an analytical solution and numerical methods need to be used to approximate the solution.
5. How can the Frobenius Equation 1 be applied in real-world problems?
The Frobenius Equation 1 has numerous real-world applications, particularly in engineering and physics. It can be used to model heat transfer in materials, study the behavior of waves in different mediums, and solve problems involving quantum mechanics. It is also used in financial mathematics to model stock prices and in computer science for optimization problems.
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