What is the solution for y^{'''}-7y^{''}-8y^'=0 ?

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

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y^{'''}-7y^{''}-8y^'=0

y^{^{'''}} - 7 y^{^{''}} - 8 y^{^{'}} = 0

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

Solution steps

y^{'''} (t) - 7 y^{''} (t) - 8 y^{'} (t) = 0

Solve linear ODE:

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

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

f (x) = \frac{2}{x ^{2}}, at x = 1

\frac{d}{d x} (\frac{1}{2} cos^{2} (\frac{x}{2}))

\int x^{3} \cdot cos (x^{2}) d x

\frac{d}{d x} ((4 x^{3} - 7 x)^{7})

\int x 2 x - x^{2} d x

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