What is the solution for y^{'''}-8y^{''}=0 ?

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

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y^{'''}-8y^{''}=0

y^{^{'''}} - 8 y^{^{''}} = 0

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

Solution steps

y^{'''} (t) - 8 y^{''} (t) = 0

Solve linear ODE:

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

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

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

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

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