What is the solution for y^{''}+6y+9=0 ?

The solution for y^{''}+6y+9=0 is y=c_{1}cos(sqrt(6)t)+c_{2}sin(sqrt(6)t)-3/2

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y^{''}+6y+9=0

y^{^{''}} + 6 y + 9 = 0

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

Solution steps

y^{''} (t) + 6 y + 9 = 0

Solve linear ODE:

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

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

y^{^{''}} + 3 y^{^{'}} = 6 x + 5

y^{^{''}} + 12 y = 4 e^{9 x}

0.01 y^{^{''}} - 0.06 y^{^{'}} + 0.08 y = 10 x

y^{^{''}} - y^{^{'}} - 2 y = 10, y (- 1) = 0, y^{^{'}} (- 1) = 1

y^{^{''}} - 3 y^{^{'}} + 2 y = 1

What is the solution for y^{''}+6y+9=0 ?
The solution for y^{''}+6y+9=0 is y=c_{1}cos(sqrt(6)t)+c_{2}sin(sqrt(6)t)-3/2