What is the solution for y^{'''}-12y^{''}-28y^'+480y=0 ?

The solution for y^{'''}-12y^{''}-28y^'+480y=0 is y=c_{1}e^{-6t}+c_{2}e^{8t}+c_{3}e^{10t}

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y^{'''}-12y^{''}-28y^'+480y=0

y^{^{'''}} - 12 y^{^{''}} - 28 y^{^{'}} + 480 y = 0

y = c_{1} e^{- 6 t} + c_{2} e^{8 t} + c_{3} e^{10 t}

Solution steps

y^{'''} (t) - 12 y^{''} (t) - 28 y^{'} (t) + 480 y = 0

Solve linear ODE:

y = c_{1} e^{- 6 t} + c_{2} e^{8 t} + c_{3} e^{10 t}

y = c_{1} e^{- 6 t} + c_{2} e^{8 t} + c_{3} e^{10 t}

What is the solution for y^{'''}-12y^{''}-28y^'+480y=0 ?
The solution for y^{'''}-12y^{''}-28y^'+480y=0 is y=c_{1}e^{-6t}+c_{2}e^{8t}+c_{3}e^{10t}