Yup, still doing DE!

Calculus Level 4

\[\large \dddot y - 2 \ddot y - 5 \dot y +6y=0\]

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 \( a_1\), \(a_2\) and \(a_3\) are real constants, and \(a\), \(b\) and \(c\) are integers, find \( a+b+c\).

Notations: \( \dot y =\dfrac { dy }{ dt }\), \(\ddot y =\dfrac { { d }^{ 2 }y }{ d{ t }^{ 2 } }\), \( \dddot y =\dfrac { { d }^{ 3 }y }{ d{ t }^{ 3 } } \).

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