Thread: Second Order Differential Equation
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Old November 1st, 2009, 05:40 PM
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Originally Posted by jen81 View Post
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.

(A - B/n)Q - A(C-n)dQ/dn + d2Q/dn2 = 0

Thank you very much.
\frac{d^2Q}{dn^2} - A(C - n)\frac{dQ}{dn} + \left(A - \frac{B}{n}\right)Q = 0.


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

m^2 - A(C - n)m + \left(A - \frac{B}{n}\right)Q = 0.


Solve this Quadratic equation for m.

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.
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