What is the solution for y^{'''}-17y^{''}+40y^'+300y=0 ?

The solution for y^{'''}-17y^{''}+40y^'+300y=0 is y=c_{1}e^{-3t}+c_{2}e^{10t}+c_{3}te^{10t}

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y^{'''}-17y^{''}+40y^'+300y=0

y^{^{'''}} - 17 y^{^{''}} + 40 y^{^{'}} + 300 y = 0

y = c_{1} e^{- 3 t} + c_{2} e^{10 t} + c_{3} t e^{10 t}

Solution steps

y^{'''} (t) - 17 y^{''} (t) + 40 y^{'} (t) + 300 y = 0

Solve linear ODE:

y = c_{1} e^{- 3 t} + c_{2} e^{10 t} + c_{3} t e^{10 t}

y = c_{1} e^{- 3 t} + c_{2} e^{10 t} + c_{3} t e^{10 t}

y^{^{''}} + 4 y^{^{'}} = 0, y (0) = 1, y^{^{'}} (0) = - 1

\frac{24}{32} y^{^{''}} + 72 y = 0

y^{^{''}} + 2 y^{^{'}} + y = 0, y^{1} = x e^{- x}

6 y^{^{''''}} + 5 y^{^{'''}} + 25 y^{^{''}} + 20 y^{^{'}} + 4 y = 0

4 \frac{d ^{2} y}{d x ^{2}} - 12 \frac{d y}{d x} + 5 y = 0

What is the solution for y^{'''}-17y^{''}+40y^'+300y=0 ?
The solution for y^{'''}-17y^{''}+40y^'+300y=0 is y=c_{1}e^{-3t}+c_{2}e^{10t}+c_{3}te^{10t}