What is the solution for y^{''}+3y^'+5y=0 ?

The solution for y^{''}+3y^'+5y=0 is y=e^{-(3t)/2}(c_{1}cos((sqrt(11)t)/2)+c_{2}sin((sqrt(11)t)/2))

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y^{''}+3y^'+5y=0

y^{^{''}} + 3 y^{^{'}} + 5 y = 0

y = e^{- \frac{3 t}{2}} (c_{1} cos (\frac{11 t}{2}) + c_{2} sin (\frac{11 t}{2}))

Solution steps

y^{''} (t) + 3 y^{'} (t) + 5 y = 0

Solve linear ODE:

y = e^{- \frac{3 t}{2}} (c_{1} cos (\frac{11 t}{2}) + c_{2} sin (\frac{11 t}{2}))

y = e^{- \frac{3 t}{2}} (c_{1} cos (\frac{11 t}{2}) + c_{2} sin (\frac{11 t}{2}))

y^{^{''''}} - 10 y^{^{'''}} + 25 y^{^{''}} = 0

y^{^{''}} + 9 y^{^{'}} + 20 y = 0

(4 D^{5} - 23 D^{3} - 33 D^{2} - 17 D - 3) y = 0

\frac{d ^{2} x}{d t ^{2}} + 5 \frac{d x}{d t} + 4 x = 0

y^{^{''}} - 7 y^{^{'}} = 0

What is the solution for y^{''}+3y^'+5y=0 ?
The solution for y^{''}+3y^'+5y=0 is y=e^{-(3t)/2}(c_{1}cos((sqrt(11)t)/2)+c_{2}sin((sqrt(11)t)/2))