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How do I know whether a differential equation is homogeneous or not? autonomous or not?

For example: $Y'=ce^4t-kY$, where $c$ and $k$ is constants. What kind of differential equation is this? Can I solve it by finding homogeneous solution plus particular solution? Thanks

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If $ce^4t$ is in fact $ce^{4t}$ then the answer is yes, you can solve it by finding general solution to the homogeneous plus a particular solution. This is a linear eqation. – Artem Dec 8 '12 at 1:33

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