What is the solution for 50x^{''}+100x^'+1000x=0 ?

The solution for 50x^{''}+100x^'+1000x=0 is x=e^{-t}(c_{1}cos(sqrt(19)t)+c_{2}sin(sqrt(19)t))

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50x^{''}+100x^'+1000x=0

50 x^{^{''}} + 100 x^{^{'}} + 1000 x = 0

x = e^{- t} (c_{1} cos (19 t) + c_{2} sin (19 t))

Solution steps

50 x^{''} (t) + 100 x^{'} (t) + 1000 x = 0

Solve linear ODE:

x = e^{- t} (c_{1} cos (19 t) + c_{2} sin (19 t))

x = e^{- t} (c_{1} cos (19 t) + c_{2} sin (19 t))

\frac{1}{10} y^{^{''}} + 11 y^{^{'}} + 24 y = 0, y (0) = 1, y^{^{'}} (0) = 0

q^{^{''}} + 6 q^{^{'}} + 9 q = 0

0.1 y^{^{''}} + 4 y^{^{'}} + 250 y = 0

125 y^{^{''}} + 30 y^{^{'}} + 500 y = 0

x^{^{''}} + 1 0^{6} x^{^{'}} - 1.6 \cdot 1 0^{11} x = 0

What is the solution for 50x^{''}+100x^'+1000x=0 ?
The solution for 50x^{''}+100x^'+1000x=0 is x=e^{-t}(c_{1}cos(sqrt(19)t)+c_{2}sin(sqrt(19)t))