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

The solution for y^{'''}-y^{''}-12y^'=0 is y=c_{1}+c_{2}e^{-3t}+c_{3}e^{4t}

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y^{'''}-y^{''}-12y^'=0

y^{^{'''}} - y^{^{''}} - 12 y^{^{'}} = 0

y = c_{1} + c_{2} e^{- 3 t} + c_{3} e^{4 t}

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- 3 t} + c_{3} e^{4 t}

y = c_{1} + c_{2} e^{- 3 t} + c_{3} e^{4 t}

x^{^{''}} + 4 k^{2} x = 0

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

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 13, y (1) = 0

x^{^{''}} + 6 x^{^{'}} + 8 x = 0

4 y^{^{''}} - 4 y^{^{'}} + 3 y = 0, y (0) = 1, y^{^{'}} (0) = 5

What is the solution for y^{'''}-y^{''}-12y^'=0 ?
The solution for y^{'''}-y^{''}-12y^'=0 is y=c_{1}+c_{2}e^{-3t}+c_{3}e^{4t}