# 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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