# 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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