What is the solution for y^{''}-6y^'-16y=0 ?

The solution for y^{''}-6y^'-16y=0 is y=c_{1}e^{8t}+c_{2}e^{-2t}

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y^{''}-6y^'-16y=0

y^{^{''}} - 6 y^{^{'}} - 16 y = 0

y = c_{1} e^{8 t} + c_{2} e^{- 2 t}

Solution steps

y^{''} (t) - 6 y^{'} (t) - 16 y = 0

Solve linear ODE:

y = c_{1} e^{8 t} + c_{2} e^{- 2 t}

y = c_{1} e^{8 t} + c_{2} e^{- 2 t}

\frac{d}{d x} (4 x^{0.75} \cdot (240 - 2 x)^{0.5})

\int_{- 3}^{- 1} \frac{5}{x ^{4}} d x

f (x) = \frac{27}{5 x ^{2}} - \frac{3}{2}, at x = 1

\int_{1}^{5} \frac{x ^{2} + 5}{6 x - x ^{2}} d x

\frac{d y}{d x} = \frac{( x y + x )}{y}

What is the solution for y^{''}-6y^'-16y=0 ?
The solution for y^{''}-6y^'-16y=0 is y=c_{1}e^{8t}+c_{2}e^{-2t}