What is the solution for (d^2x)/(dt^2)-2(dx)/(dt)-15x=0 ?

The solution for (d^2x)/(dt^2)-2(dx)/(dt)-15x=0 is x=c_{1}e^{5t}+c_{2}e^{-3t}

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(d^2x)/(dt^2)-2(dx)/(dt)-15x=0

\frac{d ^{2} x}{d t ^{2}} - 2 \frac{d x}{d t} - 15 x = 0

x = c_{1} e^{5 t} + c_{2} e^{- 3 t}

Solution steps

\frac{d ^{2} x}{d t ^{2}} - 2 \frac{d x}{d t} - 15 x = 0

Solve linear ODE:

x = c_{1} e^{5 t} + c_{2} e^{- 3 t}

x = c_{1} e^{5 t} + c_{2} e^{- 3 t}

\frac{d ^{2} y}{d t ^{2}} - 20 \frac{d y}{d t} + 100 y = 0

y^{^{''}} - 10 y^{^{'}} - 171 y = 0, y (0) = 9, y^{^{'}} (0) = 3

y^{^{''}} - 19 y^{^{'}} - 10 y = 0, y (0) = 1, y^{^{'}} (0) = - 1

y^{^{''}} + 9 y = 0, y (\frac{π}{2}) = 6, y^{^{'}} (0) = 0

y^{^{''}} + 4 y^{^{'}} + 29 y = 0, y (0) = 4

What is the solution for (d^2x)/(dt^2)-2(dx)/(dt)-15x=0 ?
The solution for (d^2x)/(dt^2)-2(dx)/(dt)-15x=0 is x=c_{1}e^{5t}+c_{2}e^{-3t}