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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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