What is the solution for 2y^{''}+4y^'+5y=0 ?

The solution for 2y^{''}+4y^'+5y=0 is y=e^{-t}(c_{1}cos(sqrt(3/2)t)+c_{2}sin(sqrt(3/2)t))

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2y^{''}+4y^'+5y=0

2 y^{^{''}} + 4 y^{^{'}} + 5 y = 0

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

Solution steps

2 y^{''} (t) + 4 y^{'} (t) + 5 y = 0

Solve linear ODE:

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

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

What is the solution for 2y^{''}+4y^'+5y=0 ?
The solution for 2y^{''}+4y^'+5y=0 is y=e^{-t}(c_{1}cos(sqrt(3/2)t)+c_{2}sin(sqrt(3/2)t))