What is the solution for 100y^{''}+80y^'+65y=0 ?

The solution for 100y^{''}+80y^'+65y=0 is y=e^{-(2t)/5}(c_{1}cos((7t)/(10))+c_{2}sin((7t)/(10)))

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100y^{''}+80y^'+65y=0

100 y^{^{''}} + 80 y^{^{'}} + 65 y = 0

y = e^{- \frac{2 t}{5}} (c_{1} cos (\frac{7 t}{10}) + c_{2} sin (\frac{7 t}{10}))

Solution steps

100 y^{''} (t) + 80 y^{'} (t) + 65 y = 0

Solve linear ODE:

y = e^{- \frac{2 t}{5}} (c_{1} cos (\frac{7 t}{10}) + c_{2} sin (\frac{7 t}{10}))

y = e^{- \frac{2 t}{5}} (c_{1} cos (\frac{7 t}{10}) + c_{2} sin (\frac{7 t}{10}))

y^{^{''}} + y = y^{^{'}}

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

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 9 y = 0, y (0) = 0

y^{^{''}} - 6 y^{^{'}} + 12 y = 0, y (0) = 0, y^{^{'}} (0) = - 7

8 y^{^{''}} + y^{^{'}} - y = 0

What is the solution for 100y^{''}+80y^'+65y=0 ?
The solution for 100y^{''}+80y^'+65y=0 is y=e^{-(2t)/5}(c_{1}cos((7t)/(10))+c_{2}sin((7t)/(10)))