What is the solution for y^{'''}-y^{''}-56y^'=0 ?

The solution for y^{'''}-y^{''}-56y^'=0 is y=c_{1}+c_{2}e^{-7t}+c_{3}e^{8t}

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y^{'''}-y^{''}-56y^'=0

y^{^{'''}} - y^{^{''}} - 56 y^{^{'}} = 0

y = c_{1} + c_{2} e^{- 7 t} + c_{3} e^{8 t}

Solution steps

y^{'''} (t) - y^{''} (t) - 56 y^{'} (t) = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{- 7 t} + c_{3} e^{8 t}

y = c_{1} + c_{2} e^{- 7 t} + c_{3} e^{8 t}

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

4 y^{^{''}} - 16 y^{^{'}} + 17 y = 0

y^{^{''}} - 7 y^{^{'}} + 12 y = 0, y (0) = 0, y (0) = 3

y^{^{''}} + (a - 1) y^{^{'}} + b y = 0

y^{^{'''}} + 3 y^{^{''}} = 0

What is the solution for y^{'''}-y^{''}-56y^'=0 ?
The solution for y^{'''}-y^{''}-56y^'=0 is y=c_{1}+c_{2}e^{-7t}+c_{3}e^{8t}