What is the solution for y^{''}+18y^'+81y=0 ?

The solution for y^{''}+18y^'+81y=0 is y=c_{1}e^{-9t}+c_{2}te^{-9t}

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y^{''}+18y^'+81y=0

y^{^{''}} + 18 y^{^{'}} + 81 y = 0

y = c_{1} e^{- 9 t} + c_{2} t e^{- 9 t}

Solution steps

y^{''} (t) + 18 y^{'} (t) + 81 y = 0

Solve linear ODE:

y = c_{1} e^{- 9 t} + c_{2} t e^{- 9 t}

y = c_{1} e^{- 9 t} + c_{2} t e^{- 9 t}

\int_{0}^{\frac{3 π}{2}} cos^{3} (25 x) d x

5 x^{^{'}} - 4 x = 0

x \to 1 lim (\frac{( 6 x - 1 )}{x - 1})

y^{^{''}} + 10 y^{^{'}} + 9 y = 9

\int_{0}^{6} \frac{x - 1}{x + 1} d x

What is the solution for y^{''}+18y^'+81y=0 ?
The solution for y^{''}+18y^'+81y=0 is y=c_{1}e^{-9t}+c_{2}te^{-9t}