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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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