What is the solution for y^{'''}+6y^{''}-16y^'=0 ?

The solution for y^{'''}+6y^{''}-16y^'=0 is y=c_{1}+c_{2}e^{2t}+c_{3}e^{-8t}

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y^{'''}+6y^{''}-16y^'=0

y^{^{'''}} + 6 y^{^{''}} - 16 y^{^{'}} = 0

y = c_{1} + c_{2} e^{2 t} + c_{3} e^{- 8 t}

Solution steps

y^{'''} (t) + 6 y^{''} (t) - 16 y^{'} (t) = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{2 t} + c_{3} e^{- 8 t}

y = c_{1} + c_{2} e^{2 t} + c_{3} e^{- 8 t}

y^{^{''}} + 2 y = 0, y (0) = 1, y^{^{'}} (0) = 1

625 x^{^{''}} + 100 x^{^{'}} + 3 x = 0, x (0) = 25, x^{^{'}} (0) = - 2

y^{^{''}} + 8 y^{^{'}} + 1 y = 0, y (0) = 3, y^{^{'}} (0) = 4

2 \cdot \frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} - 3 y = 0

u^{^{''}} + 2 r u^{^{'}} (t) + a H (t) = 0

What is the solution for y^{'''}+6y^{''}-16y^'=0 ?
The solution for y^{'''}+6y^{''}-16y^'=0 is y=c_{1}+c_{2}e^{2t}+c_{3}e^{-8t}