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Second order linear differential equations help FP2 watch

1. I dont understand why y=e^mx is the general solution of a 2nd ODE. Also, why do we substitute in the 1st and second derivatives of y=e^mx into the 2ND ODE to find the auxiliary eqn?
2. For a given second order ODE with constant coefficients:

where

Notice the above states that the addition of constant multiples of and are equal to .

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The exponential term (where a is a constant), is useful here as:

- Derrivatives of it are just a constant multiple of the exponential term,

- only where x goes to negative infinity.

So we propose as a solution to the ODE.

However, what is value a? Substitute and into the ODE to find this.

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(Note the general solution is normally of the form as a superposition of the solutions to the second order ODE but if you have a single solution for a, then the general solution is slightly different).

This is the general situation, if anyone wants to correct this then please post.

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Updated: November 2, 2017
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