What is the solution for (d^2x)/(dt^2)-4x=0 ?

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

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(d^2x)/(dt^2)-4x=0

\frac{d ^{2} x}{d t ^{2}} - 4 x = 0

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

Solution steps

\frac{d ^{2} x}{d t ^{2}} - 4 x = 0

Solve linear ODE:

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

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

x^{^{''}} - (a - 2) x^{^{'}} - (a - 1) x = 0

3 y^{^{''}} - 6 y^{^{'}} + 9 y = 0

y^{^{''}} + 25 y = 0, y (0) = 4, y^{^{'}} (0) = - 2

x^{''} + x = 0, x (\frac{π}{2}) = 0, x^{^{'}} (\frac{π}{2}) = 1

y^{^{'''''}} + 3 y^{^{''''}} + 4 y^{^{'''}} + 12 y^{^{''}} = 0

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