What is the solution for 2y^{''}+36y^'+163y=0 ?

The solution for 2y^{''}+36y^'+163y=0 is y=e^{-9t}(c_{1}cos(t/(sqrt(2)))+c_{2}sin(t/(sqrt(2))))

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2y^{''}+36y^'+163y=0

2 y^{^{''}} + 36 y^{^{'}} + 163 y = 0

y = e^{- 9 t} (c_{1} cos (\frac{t}{2}) + c_{2} sin (\frac{t}{2}))

Solution steps

2 y^{''} (t) + 36 y^{'} (t) + 163 y = 0

Solve linear ODE:

y = e^{- 9 t} (c_{1} cos (\frac{t}{2}) + c_{2} sin (\frac{t}{2}))

y = e^{- 9 t} (c_{1} cos (\frac{t}{2}) + c_{2} sin (\frac{t}{2}))

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} + 25 y = 0

y^{^{'''}} - 3 y^{^{''}} + 4 y^{^{'}} - 2 y = 0

3 y^{^{''}} + 7 y^{^{'}} + 2 y = 0

y^{^{''}} + 9 y = 0, y (0) = 0, y^{^{'}} (0) = 3

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

What is the solution for 2y^{''}+36y^'+163y=0 ?
The solution for 2y^{''}+36y^'+163y=0 is y=e^{-9t}(c_{1}cos(t/(sqrt(2)))+c_{2}sin(t/(sqrt(2))))