What is the solution for (d^2y)/(dt^2)-2(dy)/(dt)-8y=0 ?

The solution for (d^2y)/(dt^2)-2(dy)/(dt)-8y=0 is y=c_{1}e^{4t}+c_{2}e^{-2t}

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(d^2y)/(dt^2)-2(dy)/(dt)-8y=0

\frac{d ^{2} y}{d t ^{2}} - 2 \frac{d y}{d t} - 8 y = 0

y = c_{1} e^{4 t} + c_{2} e^{- 2 t}

Solution steps

\frac{d ^{2} y}{d t ^{2}} - 2 \frac{d y}{d t} - 8 y = 0

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2} e^{- 2 t}

y = c_{1} e^{4 t} + c_{2} e^{- 2 t}

\frac{d}{d x} ((x^{3} + 2 x - 5)^{2})

ln (1 - 2 x)

\int_{- π}^{π} e^{x} d x

\frac{d}{d x} (x^{4} (3 - x)^{3})

\int 1 - tan^{2} (x) d x

What is the solution for (d^2y)/(dt^2)-2(dy)/(dt)-8y=0 ?
The solution for (d^2y)/(dt^2)-2(dy)/(dt)-8y=0 is y=c_{1}e^{4t}+c_{2}e^{-2t}