What is the solution for y4+3y^{''}+y=0 ?

The solution for y4+3y^{''}+y=0 is y=c_{1}cos(sqrt(5/3)t)+c_{2}sin(sqrt(5/3)t)

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y4+3y^{''}+y=0

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

y = c_{1} cos (\frac{5}{3} t) + c_{2} sin (\frac{5}{3} t)

Solution steps

y 4 + 3 y^{''} (t) + y = 0

Solve linear ODE:

y = c_{1} cos (\frac{5}{3} t) + c_{2} sin (\frac{5}{3} t)

y = c_{1} cos (\frac{5}{3} t) + c_{2} sin (\frac{5}{3} t)

y^{^{''}} + \frac{8}{100} y^{^{'}} + \frac{12}{10000} y = 0

y^{^{''}} - y = 0, y (ln (2)) = 5, y (0) = 1

\frac{d ^{2} x}{d t ^{2}} + 4 \frac{d x}{d t} + 2 x = 0, x (0) = 0

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

2 \cdot y^{^{''}} + 8 \cdot y^{^{'}} + 8 y = 0

What is the solution for y4+3y^{''}+y=0 ?
The solution for y4+3y^{''}+y=0 is y=c_{1}cos(sqrt(5/3)t)+c_{2}sin(sqrt(5/3)t)