What is the solution for y^{''}+16y=0,y(0)=2,y^{''}(0)=-2 ?

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

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y^{''}+16y=0,y(0)=2,y^{''}(0)=-2

y^{^{''}} + 16 y = 0, y (0) = 2, y^{^{''}} (0) = - 2

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{'''}} + y^{^{''}} - 16 y^{^{'}} + 20 y = 0

3 y^{^{''}} + 5 y^{^{'}} + y = 0

y^{^{''}} + 16 y = 0, y (0) = 3, y^{^{'}} (0) = 1

y^{^{''}} + 16 y = 0, y (0) = 3, y^{^{'}} (0) = 0

y^{^{'''}} + 4 y^{^{''}} + 5 y^{^{'}} + 2 y = 0

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