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})

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)