What is the solution for y^{''}+2sqrt(14)y^'+14y=0 ?

The solution for y^{''}+2sqrt(14)y^'+14y=0 is y=c_{1}e^{-sqrt(14)t}+c_{2}te^{-sqrt(14)t}

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y^{''}+2sqrt(14)y^'+14y=0

y^{^{''}} + 214 y^{^{'}} + 14 y = 0

y = c_{1} e^{- 14 t} + c_{2} t e^{- 14 t}

Solution steps

y^{''} (t) + 214 y^{'} (t) + 14 y = 0

Solve linear ODE:

y = c_{1} e^{- 14 t} + c_{2} t e^{- 14 t}

y = c_{1} e^{- 14 t} + c_{2} t e^{- 14 t}

y^{^{'}} + \frac{3}{x} y = x^{2} y^{2}

\frac{\partial}{\partial x} (e^{3 x} cos (2 x))

\int \frac{1}{x ^{4}} d x

\frac{d}{d x} (\frac{x ^{2}}{1 + x})

\frac{5}{x + 1}

What is the solution for y^{''}+2sqrt(14)y^'+14y=0 ?
The solution for y^{''}+2sqrt(14)y^'+14y=0 is y=c_{1}e^{-sqrt(14)t}+c_{2}te^{-sqrt(14)t}