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[tex]ay+b\int^y_0ydy+cy'=0[/tex]

then

[tex]ay'+by+cy''=0[/tex]

now, let

[tex]y=e^{sx}[/tex]

thus,

[tex]s^2+a/cs+b/c=0[/tex]

and then one solves for s. It is then plugged into what sources are deeming a "general solution"

[tex]y=C_1e^{s_1x}+C_2e^{s_2x}[/tex]

however, none of these texbooks explain or derive where this comes from, and I have not taken any linear algebra or differential equations. Can someone explain where [tex]y=C_1e^{s_1x}+C_2e^{s_2x}[/tex] comes from?

Thanks!

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# Second Order Linear ODEs

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