Yup, still doing DE!

Calculus Level 4

\[ \overset {... }{ y } -2 \overset { .. }{ y } - 5 \overset {. }{ y } +6y=0\]

If the above differential equation has the general solution of the form \(y = { a }_{ 1 }{ e }^{ at }+{ a }_{ 2 }{ e }^{ bt }+{ a }_{ 3 }{ e }^{ ct }\), where \( a_1, a_2, a_3 \) are real constants and \(a, b, c\) are integers, find \( a+b+c\).

Note: \( \overset { . }{ y } =\frac { dy }{ dt }\), \(\overset { .. }{ y } =\frac { { d }^{ 2 }y }{ d{ t }^{ 2 } }\), \( \overset { ... }{ y } =\frac { { d }^{ 3 }y }{ d{ t }^{ 3 } } \).

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