What is the solution for (d^2x)/(dt^2)-(dx)/(dt)-2x=0 ?

The solution for (d^2x)/(dt^2)-(dx)/(dt)-2x=0 is x=c_{1}e^{2t}+c_{2}e^{-t}

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(d^2x)/(dt^2)-(dx)/(dt)-2x=0

\frac{d ^{2} x}{d t ^{2}} - \frac{d x}{d t} - 2 x = 0

x = c_{1} e^{2 t} + c_{2} e^{- t}

Solution steps

\frac{d ^{2} x}{d t ^{2}} - \frac{d x}{d t} - 2 x = 0

Solve linear ODE:

x = c_{1} e^{2 t} + c_{2} e^{- t}

x = c_{1} e^{2 t} + c_{2} e^{- t}

7 y^{^{''}} + 7 y = 0

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

y^{^{''}} + 3 y^{^{'}} + 2 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 7 y^{^{'}} + 12 y = 0, y (0) = 1, y^{^{'}} (0) = 2

y^{^{'''}} + y^{^{'}} = 0, y (0) = 0, y^{^{'}} (0) = 1, y^{^{''}} (0) = 2

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