What is the solution for y^{''}+16y=0,y(0)=1,y^'(0)=0 ?

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

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

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

y = cos (4 t)

Solution steps

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

Solve linear ODE:

y = cos (4 t)

y = cos (4 t)

y^{^{''}} + 11 y^{^{'}} - 12 y = 0

10 y^{^{''}} + 9 y^{^{'}} + 2 y = 0

y^{^{''}} - 2 y^{^{'}} + y = 0, y (0) = 5, y^{^{'}} (0) = 1

y^{^{''}} - 8 y^{^{'}} + α y = 0, y (0) = 1, y^{^{'}} (0) = 13

y^{^{''}} + 3^{2} y = 0

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