What is the solution for y^{'''}+6y^{''}-15y^'+8y=0 ?

The solution for y^{'''}+6y^{''}-15y^'+8y=0 is y=c_{1}e^{-8t}+c_{2}e^t+c_{3}te^t

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y^{'''}+6y^{''}-15y^'+8y=0

y^{^{'''}} + 6 y^{^{''}} - 15 y^{^{'}} + 8 y = 0

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

Solution steps

y^{'''} (t) + 6 y^{''} (t) - 15 y^{'} (t) + 8 y = 0

Solve linear ODE:

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

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

\frac{d}{d x} (\frac{x ^{2}}{9 + 4 x})

\int_{\frac{1}{7}}^{5} 8 x ln (7 x) d x

f^{^{'}} (x) = x (x - 3)

3 x y^{2}

\frac{\partial}{\partial z} (ln (x^{2} + y^{2} + z^{2}))

What is the solution for y^{'''}+6y^{''}-15y^'+8y=0 ?
The solution for y^{'''}+6y^{''}-15y^'+8y=0 is y=c_{1}e^{-8t}+c_{2}e^t+c_{3}te^t