# Math Help - Homogeneous linear ODEs with Constant Coefficients

1. ## Homogeneous linear ODEs with Constant Coefficients

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do you have a idea about it?can you help me

http://img17.imageshack.us/img17/1156/18176658.png

2. ## Re: Homogeneous linear ODEs with Constant Coefficients

Originally Posted by oasi
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do you have a idea about it?can you help me
Homogenous equations with constant coefficients

3. ## Re: Homogeneous linear ODEs with Constant Coefficients

Originally Posted by oasi
1.bmp

do you have a idea about it?can you help me

http://img17.imageshack.us/img17/1156/18176658.png
You're looking for a particular function, which, when added or subtracted with scalar multiples of its derivatives, will end up as 0. This means that the particular function and its derivatives need to be of the same "family". The exponential function is an obvious choice, because the exponential function is its own derivative (i.e. the derivatives will be in the same family).