Characteristic equation from an exponential trial solution (Q1621)

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Characteristic equation from an exponential trial solution
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    Statements

    y=e^{rx}\\ \\Rightarrow\\ (r^{2}-3r+2)\\,e^{rx}=0\\ \\Rightarrow\\ r^{2}-3r+2=(r-1)(r-2)=0
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