Finding a General Solution

**tigergirl** · March 2nd 2010, 06:56 PM

Find the general solution of a 4th order linear homogenous d.e. with real number coefficients if two soultions are $y_{1} = xe^{-2x}$ and $y_{2} = xe^{x}$ .

**TheEmptySet** · March 5th 2010, 06:55 PM

Originally Posted by tigergirl

Find the general solution of a 4th order linear homogenous d.e. with real number coefficients if two soultions are $y_{1} = xe^{-2x}$ and $y_{2} = xe^{x}$ .

So you know that the auxillary equaiton is degree 4.

$y_1$ represents the solution to a degree to of the form
$(m+2)^2$ and $y_2$ is of the form $(m-1)^2$

so the other two solutions are $c_1e^{-2x} \text{ and } c_2e^{x}$

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