What is the solution for x^{''}+0.5*x^'+17/16*x=0 ?

The solution for x^{''}+0.5*x^'+17/16*x=0 is x=e^{-0.25t}(c_{1}cos(t)+c_{2}sin(t))

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x^{''}+0.5x^'+17/16x=0

x^{^{''}} + 0.5 \cdot x^{^{'}} + \frac{17}{16} \cdot x = 0

x = e^{- 0.25 t} (c_{1} cos (t) + c_{2} sin (t))

Solution steps

x^{''} (t) + 0.5 \cdot x^{'} (t) + \frac{17}{16} \cdot x = 0

Solve linear ODE:

x = e^{- 0.25 t} (c_{1} cos (t) + c_{2} sin (t))

x = e^{- 0.25 t} (c_{1} cos (t) + c_{2} sin (t))

3 x^{^{''}} + 2 x^{^{'}} + 3 x = 0

4 y^{^{''}} + 12 y^{^{'}} + 9 y = 0, y (0) = 1, y^{^{'}} (0) = - 4

y^{^{''}} + 5 y^{^{'}} = 0, y (0) = 5, y^{^{'}} (0) = - 20

y^{^{''}} + 4 y^{^{'}} + 7 y = 0, y (0) = 1, y^{^{'}} (0) = - 2

y^{^{''}} - 2 y^{^{'}} - 3 y = 0, y (0) = 0, y^{^{'}} (0) = - 4

What is the solution for x^{''}+0.5*x^'+17/16*x=0 ?
The solution for x^{''}+0.5*x^'+17/16*x=0 is x=e^{-0.25t}(c_{1}cos(t)+c_{2}sin(t))