What is the solution for y^{''}+16y=cos(4t),y(0)=3,y^'(0)=2 ?

The solution for y^{''}+16y=cos(4t),y(0)=3,y^'(0)=2 is y=3cos(4t)+1/2 sin(4t)+(tsin(4t))/8

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y^{''}+16y=cos(4t),y(0)=3,y^'(0)=2

y^{^{''}} + 16 y = cos (4 t), y (0) = 3, y^{^{'}} (0) = 2

y = 3 cos (4 t) + \frac{1}{2} sin (4 t) + \frac{t sin ( 4 t )}{8}

Solution steps

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

Solve linear ODE:

y = 3 cos (4 t) + \frac{1}{2} sin (4 t) + \frac{t sin ( 4 t )}{8}

y = 3 cos (4 t) + \frac{1}{2} sin (4 t) + \frac{t sin ( 4 t )}{8}

What is the solution for y^{''}+16y=cos(4t),y(0)=3,y^'(0)=2 ?
The solution for y^{''}+16y=cos(4t),y(0)=3,y^'(0)=2 is y=3cos(4t)+1/2 sin(4t)+(tsin(4t))/8