What is the solution for y^{''}+6y^'+45y=0 ?

The solution for y^{''}+6y^'+45y=0 is y=e^{-3t}(c_{1}cos(6t)+c_{2}sin(6t))

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y^{''}+6y^'+45y=0

y^{^{''}} + 6 y^{^{'}} + 45 y = 0

y = e^{- 3 t} (c_{1} cos (6 t) + c_{2} sin (6 t))

Solution steps

y^{''} (t) + 6 y^{'} (t) + 45 y = 0

Solve linear ODE:

y = e^{- 3 t} (c_{1} cos (6 t) + c_{2} sin (6 t))

y = e^{- 3 t} (c_{1} cos (6 t) + c_{2} sin (6 t))

y = (x + 9) (3 x + 4)

\int (3 x - 2 3 x) d x

5

\int (x - 3 y^{2}) d y

\frac{d}{d x} (\frac{tan ( x )}{6 x sec ( x )})

What is the solution for y^{''}+6y^'+45y=0 ?
The solution for y^{''}+6y^'+45y=0 is y=e^{-3t}(c_{1}cos(6t)+c_{2}sin(6t))