What is the solution for y^{'''}-9y^{''}+15y^'+25y=0 ?

The solution for y^{'''}-9y^{''}+15y^'+25y=0 is y=c_{1}e^{-t}+c_{2}e^{5t}+c_{3}te^{5t}

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y^{'''}-9y^{''}+15y^'+25y=0

y^{^{'''}} - 9 y^{^{''}} + 15 y^{^{'}} + 25 y = 0

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

Solution steps

y^{'''} (t) - 9 y^{''} (t) + 15 y^{'} (t) + 25 y = 0

Solve linear ODE:

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

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

\frac{\partial}{\partial x} (\frac{x}{v})

x \to 8 + lim (\frac{∣ x - 8 ∣}{x - 8})

\frac{d}{d x} (\frac{5 x ^{3} - 7}{x})

f (x) = 10 cos (30 x - 7)

\int \frac{- 2 x}{1 + x ^{2}} d x

What is the solution for y^{'''}-9y^{''}+15y^'+25y=0 ?
The solution for y^{'''}-9y^{''}+15y^'+25y=0 is y=c_{1}e^{-t}+c_{2}e^{5t}+c_{3}te^{5t}