What is the solution for y^{''}+sqrt(80)y^'+20y=0 ?

The solution for y^{''}+sqrt(80)y^'+20y=0 is y=c_{1}e^{-2sqrt(5)t}+c_{2}te^{-2sqrt(5)t}

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y^{''}+sqrt(80)y^'+20y=0

y^{^{''}} + 80 y^{^{'}} + 20 y = 0

y = c_{1} e^{- 25 t} + c_{2} t e^{- 25 t}

Solution steps

y^{''} (t) + 80 y^{'} (t) + 20 y = 0

Solve linear ODE:

y = c_{1} e^{- 25 t} + c_{2} t e^{- 25 t}

y = c_{1} e^{- 25 t} + c_{2} t e^{- 25 t}

\int \frac{( - 2 u ^{4} + 3 u )}{u ^{2}} d u

x \to \frac{1}{4} lim (x^{2} + 3 x)

\frac{d}{d x} (- \frac{3 e ^{\frac{3}{x}}}{x ^{2}})

f (x) = 21 x^{3} ln (x)

\int \frac{2 x ^{4} + 2 5 x}{x} d x

What is the solution for y^{''}+sqrt(80)y^'+20y=0 ?
The solution for y^{''}+sqrt(80)y^'+20y=0 is y=c_{1}e^{-2sqrt(5)t}+c_{2}te^{-2sqrt(5)t}