What is the solution for y^{''}+0.025*y+0.1y^'=0 ?

The solution for y^{''}+0.025*y+0.1y^'=0 is y=e^{-t/(20)}(c_{1}cos((3t)/(20))+c_{2}sin((3t)/(20)))

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y^{''}+0.025*y+0.1y^'=0

y^{^{''}} + 0.025 \cdot y + 0.1 y^{^{'}} = 0

y = e^{- \frac{t}{20}} (c_{1} cos (\frac{3 t}{20}) + c_{2} sin (\frac{3 t}{20}))

Solution steps

y^{''} (t) + 0.025 \cdot y + 0.1 y^{'} (t) = 0

Solve linear ODE:

y = e^{- \frac{t}{20}} (c_{1} cos (\frac{3 t}{20}) + c_{2} sin (\frac{3 t}{20}))

y = e^{- \frac{t}{20}} (c_{1} cos (\frac{3 t}{20}) + c_{2} sin (\frac{3 t}{20}))

(D^{3} - 3 D - 2) y = 0

y^{^{''}} + 16 y = 0, y^{^{'}} (0) = - 2, y (0) = 2

y^{^{''}} - 4 y = 0, y (0) = 0, y^{^{'}} (0) = 5

8 y^{^{''}} + c y^{^{'}} + 128 y = 0, y (0) = 5, y^{^{'}} (0) = 8

y^{^{''}} - 4 y = 0, y (0) = 0, y^{^{'}} (0) = 6

What is the solution for y^{''}+0.025*y+0.1y^'=0 ?
The solution for y^{''}+0.025*y+0.1y^'=0 is y=e^{-t/(20)}(c_{1}cos((3t)/(20))+c_{2}sin((3t)/(20)))