What is the solution for 100y^{''}+200y^'+101y=0 ?

The solution for 100y^{''}+200y^'+101y=0 is y=e^{-t}(c_{1}cos(t/(10))+c_{2}sin(t/(10)))

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100y^{''}+200y^'+101y=0

100 y^{^{''}} + 200 y^{^{'}} + 101 y = 0

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

Solution steps

100 y^{''} (t) + 200 y^{'} (t) + 101 y = 0

Solve linear ODE:

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

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

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

\frac{d ^{2} x}{d t ^{2}} + 8 \frac{d x}{d t} + 4 x = 0

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

y^{^{''}} - 6 y^{^{'}} + 90 y = 0

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 9 y = 0

What is the solution for 100y^{''}+200y^'+101y=0 ?
The solution for 100y^{''}+200y^'+101y=0 is y=e^{-t}(c_{1}cos(t/(10))+c_{2}sin(t/(10)))