What is the solution for 81y^{''}=-16y,y(0)=cos(kt) ?

The solution for 81y^{''}=-16y,y(0)=cos(kt) is y=c_{1}cos((4t)/9)+c_{2}sin((4t)/9)

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81y^{''}=-16y,y(0)=cos(kt)

81 y^{^{''}} = - 16 y, y (0) = cos (k t)

y = c_{1} cos (\frac{4 t}{9}) + c_{2} sin (\frac{4 t}{9})

Solution steps

81 y^{''} (t) = - 16 y

Solve linear ODE:

y = c_{1} cos (\frac{4 t}{9}) + c_{2} sin (\frac{4 t}{9})

y = c_{1} cos (\frac{4 t}{9}) + c_{2} sin (\frac{4 t}{9})

3 y^{^{''}} - 15 y^{^{'}} + 18 y = 0

y^{^{'''}} + 5 y^{^{''}} - 4 y^{^{'}} - 60 y = 0

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

y^{^{''}} + 10 y^{^{'}} + 26 y = 0, y (0) = 1, y^{^{'}} (0) = 0

\frac{d ^{2} y}{d x ^{2}} + a^{2} y = 0

What is the solution for 81y^{''}=-16y,y(0)=cos(kt) ?
The solution for 81y^{''}=-16y,y(0)=cos(kt) is y=c_{1}cos((4t)/9)+c_{2}sin((4t)/9)