What is the solution for linear y^{''}+16y=0,y(0)=sin(kt) ?

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

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linear y^{''}+16y=0,y(0)=sin(kt)

linear

y^{^{''}} + 16 y = 0, y (0) = sin (k t)

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

Solution steps

y^{''} (t) + 16 y = 0

Solve linear ODE:

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

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

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

y^{^{''}} + 2 y^{^{'}} - 3 y = 0, y^{^{'}} (0) = 0

36 y^{^{''}} + 156 y^{^{'}} + 169 y = 0, y (0) = 9, y^{^{'}} (0) = 4

y^{^{''}} - 6 y = 0, y (0) = 0, y (1) = 0

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

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