What is the solution for y^{'''}-6y^'-7=0 ?

The solution for y^{'''}-6y^'-7=0 is y=c_{1}+c_{2}e^{-sqrt(6)t}+c_{3}e^{sqrt(6)t}-(7t)/6

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y^{'''}-6y^'-7=0

y^{^{'''}} - 6 y^{^{'}} - 7 = 0

y = c_{1} + c_{2} e^{- 6 t} + c_{3} e^{6 t} - \frac{7 t}{6}

Solution steps

y^{'''} (t) - 6 y^{'} (t) - 7 = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{- 6 t} + c_{3} e^{6 t} - \frac{7 t}{6}

y = c_{1} + c_{2} e^{- 6 t} + c_{3} e^{6 t} - \frac{7 t}{6}

\frac{d ^{2} y}{d x ^{2}} + 9 y = 15 x^{2} - 9

y^{^{''}} + 6 y^{^{'}} + 8 y = 2 t + e^{t}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{x}}{x}, y (1) = 0, y^{^{'}} (1) = 1

y^{^{''}} + y^{^{'}} + 4 y = e^{- 1.3 t}

y^{^{''}} + 3 y^{^{'}} + 2 y = 3 e^{- 2 x} + x

What is the solution for y^{'''}-6y^'-7=0 ?
The solution for y^{'''}-6y^'-7=0 is y=c_{1}+c_{2}e^{-sqrt(6)t}+c_{3}e^{sqrt(6)t}-(7t)/6