What is the solution for (d^2x)/(dt^2)-49x=0,x=2 ?

The solution for (d^2x)/(dt^2)-49x=0,x=2 is x=(2-c_{2})e^{7t}+c_{2}e^{-7t}

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(d^2x)/(dt^2)-49x=0,x=2

\frac{d ^{2} x}{d t ^{2}} - 49 x = 0, x = 2

x = (2 - c_{2}) e^{7 t} + c_{2} e^{- 7 t}

Solution steps

\frac{d ^{2} x}{d t ^{2}} - 49 x = 0

Solve linear ODE:

x = (2 - c_{2}) e^{7 t} + c_{2} e^{- 7 t}

x = (2 - c_{2}) e^{7 t} + c_{2} e^{- 7 t}

y^{^{''}} - 2 y^{^{'}} + y = (x 2 - 2 x) e^{-} x

- 3 y^{^{''}} + 27 y = 0, y^{^{'}} (- 2) = - 2, y (2) = - 2

y^{^{''}} + 5 y^{^{'}} = 0, y (0) = - 11, y^{^{'}} (0) = 35

12 y^{^{''}} - 11 y^{^{'}} + 2 y = 0, y (0) = 7, y^{^{'}} (0) = - 3

y^{^{''''}} - 4 y^{^{'''}} + 9 y^{^{''}} - 36 y^{^{'}} = 0

What is the solution for (d^2x)/(dt^2)-49x=0,x=2 ?
The solution for (d^2x)/(dt^2)-49x=0,x=2 is x=(2-c_{2})e^{7t}+c_{2}e^{-7t}