What is the solution for y^{''}+2*2.5*4*y^'+16y=0 ?

The solution for y^{''}+2*2.5*4*y^'+16y=0 is y=c_{1}e^{2(sqrt(21)-5)t}+c_{2}e^{-2(5+sqrt(21))t}

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y^{''}+22.54*y^'+16y=0

y^{^{''}} + 2 \cdot 2.5 \cdot 4 \cdot y^{^{'}} + 16 y = 0

y = c_{1} e^{2 (21 - 5) t} + c_{2} e^{- 2 (5 + 21) t}

Solution steps

y^{''} (t) + 2 \cdot 2.5 \cdot 4 \cdot y^{'} (t) + 16 y = 0

Solve linear ODE:

y = c_{1} e^{2 (21 - 5) t} + c_{2} e^{- 2 (5 + 21) t}

y = c_{1} e^{2 (21 - 5) t} + c_{2} e^{- 2 (5 + 21) t}

\int \frac{1}{3 + 5 cos ( x )} d x

\frac{d}{d x} (x^{3} e^{5 x})

\int (x + \frac{1}{6 x}) d x

\int_{0}^{1} x (x^{2} - x) d x

\int \frac{x}{y} d y

What is the solution for y^{''}+2*2.5*4*y^'+16y=0 ?
The solution for y^{''}+2*2.5*4*y^'+16y=0 is y=c_{1}e^{2(sqrt(21)-5)t}+c_{2}e^{-2(5+sqrt(21))t}