What is the solution for y^{'''}-6y^{''}-15y^'+100y=0 ?

The solution for y^{'''}-6y^{''}-15y^'+100y=0 is y=c_{1}e^{-4t}+c_{2}e^{5t}+c_{3}te^{5t}

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y^{'''}-6y^{''}-15y^'+100y=0

y^{^{'''}} - 6 y^{^{''}} - 15 y^{^{'}} + 100 y = 0

y = c_{1} e^{- 4 t} + c_{2} e^{5 t} + c_{3} t e^{5 t}

Solution steps

y^{'''} (t) - 6 y^{''} (t) - 15 y^{'} (t) + 100 y = 0

Solve linear ODE:

y = c_{1} e^{- 4 t} + c_{2} e^{5 t} + c_{3} t e^{5 t}

y = c_{1} e^{- 4 t} + c_{2} e^{5 t} + c_{3} t e^{5 t}

4 y^{^{''}} - 3 y^{^{'}} - 7 y = 0

y^{^{''}} + 4 y = 0, y (\frac{π}{6}) = 4, y^{^{'}} (\frac{π}{6}) = - 8

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

y^{^{'''''}} + 2 y^{^{''''}} + 4 y^{^{'''}} + 8 y^{^{''}} = 0

3 x y^{^{''}} - 20 x y^{^{'}} + 3 x y = 0

What is the solution for y^{'''}-6y^{''}-15y^'+100y=0 ?
The solution for y^{'''}-6y^{''}-15y^'+100y=0 is y=c_{1}e^{-4t}+c_{2}e^{5t}+c_{3}te^{5t}