What is the solution for 4y^{''}+3y^{''}+y=0 ?

The solution for 4y^{''}+3y^{''}+y=0 is y=c_{1}cos(t/(sqrt(7)))+c_{2}sin(t/(sqrt(7)))

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

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

y = c_{1} cos (\frac{t}{7}) + c_{2} sin (\frac{t}{7})

Solution steps

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

Solve linear ODE:

y = c_{1} cos (\frac{t}{7}) + c_{2} sin (\frac{t}{7})

y = c_{1} cos (\frac{t}{7}) + c_{2} sin (\frac{t}{7})

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

4 y^{^{''}} - 4 y^{^{'}} + (- 3) y = 0, y (0) = 5, y^{^{'}} (0) = 0

y^{^{''}} + 0.25 y = 0

y^{^{''}} - 2 y^{^{'}} + 2 y = 0, y (0) = 2, y^{^{'}} (0) = 0

x^{^{''}} - 9 x^{^{'}} - 14 x = 0

What is the solution for 4y^{''}+3y^{''}+y=0 ?
The solution for 4y^{''}+3y^{''}+y=0 is y=c_{1}cos(t/(sqrt(7)))+c_{2}sin(t/(sqrt(7)))