Hi,

I have a second order differential equation as shown below. I have no idea how to start and solve the problem. Appreciate if anyone could help me on this.

Thank you very much.

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- November 1st 2009, 05:17 PMjen81Second Order Differential Equation
Hi,

I have a second order differential equation as shown below. I have no idea how to start and solve the problem. Appreciate if anyone could help me on this.

Thank you very much. - November 1st 2009, 05:40 PMProve It
.

I'm assuming that this is a second order linear CONSTANT COEFFICIENT ODE, so write the characteristic equation:

.

Solve this Quadratic equation for .

You will end up with either:

1. Two real distinct solutions

2. Two real repeated solutions

3. Complex conjugates.

The solution to the ODE depends on the solutions of the characteristic equation. - November 2nd 2009, 01:58 AMjen81
Hi,

Thanks ProveIt.

The solution to the equation above if assuming B = 0 is

I tried the method as suggested but I couldn't get to this solution.

Thank you very much. - November 2nd 2009, 03:08 PMshawsend
The differentiation is with respect to n, albeit non-standard notation, so it's a DE with variable coefficients. And if I let B=0 and just change n to x to make it more standard looking, it's then:

So other than power series, we could get it into normal form letting:

which then gets it to:

with:

but that's as far as I can take it.