What is the solution for y^{''}+3y^'+9y=0 ?

The solution for y^{''}+3y^'+9y=0 is y=e^{-(3t)/2}(c_{1}cos((3^{3/2}t)/2)+c_{2}sin((3^{3/2}t)/2))

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y^{''}+3y^'+9y=0

y^{^{''}} + 3 y^{^{'}} + 9 y = 0

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

Solution steps

y^{''} (t) + 3 y^{'} (t) + 9 y = 0

Solve linear ODE:

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

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

h \to 6 lim (\frac{4 h}{h - 6})

\frac{d}{d x} (- tan (9 x))

x \to 0 lim ([(2 x + 1) (x - 3)])

y = 2 x + \frac{5}{x}

f (x) = ln (2 x), y = 0, y = 2

What is the solution for y^{''}+3y^'+9y=0 ?
The solution for y^{''}+3y^'+9y=0 is y=e^{-(3t)/2}(c_{1}cos((3^{3/2}t)/2)+c_{2}sin((3^{3/2}t)/2))