What is the solution for y^{'''}+8y^{''}+5y^'-50y=0 ?

The solution for y^{'''}+8y^{''}+5y^'-50y=0 is y=c_{1}e^{2t}+c_{2}e^{-5t}+c_{3}te^{-5t}

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y^{'''}+8y^{''}+5y^'-50y=0

y^{^{'''}} + 8 y^{^{''}} + 5 y^{^{'}} - 50 y = 0

y = c_{1} e^{2 t} + c_{2} e^{- 5 t} + c_{3} t e^{- 5 t}

Solution steps

y^{'''} (t) + 8 y^{''} (t) + 5 y^{'} (t) - 50 y = 0

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- 5 t} + c_{3} t e^{- 5 t}

y = c_{1} e^{2 t} + c_{2} e^{- 5 t} + c_{3} t e^{- 5 t}

(\frac{x + 2}{x - 2})^{2}

\frac{d}{d x} (e^{x t a n (x)})

y = x^{4} + 3 x^{2} - x

y^{2} = x - 1, 1, 3

What is the solution for y^{'''}+8y^{''}+5y^'-50y=0 ?
The solution for y^{'''}+8y^{''}+5y^'-50y=0 is y=c_{1}e^{2t}+c_{2}e^{-5t}+c_{3}te^{-5t}