Tagged Questions

1answer
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Finding the coefficients of the series solution of an initial value problem

I shell present 2 questions I came across today related to this subject. I need some explanation about the meaning of the IVP I am given. We look for a solution of the form $y=\sum a_nx^n$. So after ...
0answers
21 views

Find a series solution to $(x^2-2)y''+6xy'+4y=0$.

Find a series solution to $(x^2-2)y''+6xy'+4y=0$. A. Find the recurrence relation to $a_n$: My answer is $a_{n+2}=a_n\cdot \frac{n+4}{2(n+2)}$ which is correct. B. Using A, write two independent ...
3answers
40 views

1answer
42 views

Trying to find 2nd power series solution

For the equation $xy'' + 2xy' + 6e^xy = 0$, I need to find the first 3 nonzero terms in each of two linearly independent solutions about x=0. I changed this to the form of ...
2answers
73 views

Solution of the Legendre's ODE using Frobenius Method

This is the Legendre's differential equation given in my book: $(1-x)^{2}\ddot{y}-2x\dot{y}+k(k+1)y=0$ I solved this equation by taking: $y=x^{c}\{a_{0}+a_{1}x+a_{2}x^{2}+.....+a_{r}x^{r}+.....\}$ ...
0answers
33 views

Power series solution for a DE with Frobenius method

The given DE is $(x²-3)y"+2xy'=0$ Since there is a singular point ($x=\pm\sqrt{3}$) I used the Frobenius method. I found two indicial relationships: $-3r(r+1)=0$ and $-3(r+1)(r+2)=0$ because I have ...
0answers
43 views

Power series to solve differential equations?

We can use the formula $$F(x)=e^{λx} [ ρ-λμ-\dfrac{1}{2} λ^2 σ^2 ]^{-1}. (1)$$ to derive an expression for F(x) when f(x) is any integer power $x^n$. Begin by observing that for the ...
1answer
15 views

Why not shift the index of the derivative in Euler series?

I'm reading over solving linear differential equations with analytic coefficients, and finding the solutions that are near regular singular points. In the earlier section on solving similar equations ...
0answers
36 views

Radius of Convergence and the Frobenius Method

Consider the equation $$4xy'' + 2y'+ y = 0$$ I know that $x=4$ is a regular singular point, and in the notation that my uni uses, we say that: $$(x-x_0)^2 y'' + (x-x_0)p(x)y' + q(x)y = 0$$ where ...
1answer
15 views

1answer
22 views

Series Solution To Differential Equations - Need help with one step

Would someone kindly explain to me what the logic is behind one of the steps here: http://tutorial.math.lamar.edu/Classes/DE/SeriesSolutions.aspx In Example 1 - Following on from this sentence on ...
1answer
29 views