What is the solution for y^{''}+16y=3sin(8t),y(0)=0,y^'(0)=0 ?

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

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y^{''}+16y=3sin(8t),y(0)=0,y^'(0)=0

y^{^{''}} + 16 y = 3 sin (8 t), y (0) = 0, y^{^{'}} (0) = 0

y = \frac{1}{8} sin (4 t) - \frac{1}{16} sin (8 t)

Solution steps

y^{''} (t) + 16 y = 3 sin (8 t)

Solve linear ODE:

y = \frac{1}{8} sin (4 t) - \frac{1}{16} sin (8 t)

y = \frac{1}{8} sin (4 t) - \frac{1}{16} sin (8 t)

\frac{\partial}{\partial y} (\frac{3 x - 3 y}{3 x + 3 y})

x \to 0 lim (x - \frac{1}{x - 1})

\int 100 e^{0.2 x} d x

\int (2 x + 2) e^{x^{2} + 2 x} d x

\int y^{3} d y

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