What is the solution for y^{''}+16y=cos(4t),y(0)=6,y^'(0)=8 ?

The solution for y^{''}+16y=cos(4t),y(0)=6,y^'(0)=8 is y=6cos(4t)+2sin(4t)+(tsin(4t))/8

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y^{''}+16y=cos(4t),y(0)=6,y^'(0)=8

y^{^{''}} + 16 y = cos (4 t), y (0) = 6, y^{^{'}} (0) = 8

y = 6 cos (4 t) + 2 sin (4 t) + \frac{t sin ( 4 t )}{8}

Solution steps

y^{''} (t) + 16 y = cos (4 t)

Solve linear ODE:

y = 6 cos (4 t) + 2 sin (4 t) + \frac{t sin ( 4 t )}{8}

y = 6 cos (4 t) + 2 sin (4 t) + \frac{t sin ( 4 t )}{8}

y^{^{''}} + 3 y^{^{'}} + 2 y = 1, + 4 x e^{- 3 x} y (0) = 0

x^{^{''}} + x = t sin (2 t)

y^{^{''}} + 3 y^{^{'}} + 2 y = 3 x e^{- x}

y^{^{''}} + y - 1 = 0

y^{^{''}} - 6 y^{^{'}} + 5 y = t e^{2 t}

What is the solution for y^{''}+16y=cos(4t),y(0)=6,y^'(0)=8 ?
The solution for y^{''}+16y=cos(4t),y(0)=6,y^'(0)=8 is y=6cos(4t)+2sin(4t)+(tsin(4t))/8