What is the solution for y^{''}+16y=3sin(5t),y(0)=0,y^'(0)=0 ?

The solution for y^{''}+16y=3sin(5t),y(0)=0,y^'(0)=0 is y= 5/12 sin(4t)-1/3 sin(5t)

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y^{''}+16y=3sin(5t),y(0)=0,y^'(0)=0

y^{^{''}} + 16 y = 3 sin (5 t), y (0) = 0, y^{^{'}} (0) = 0

y = \frac{5}{12} sin (4 t) - \frac{1}{3} sin (5 t)

Solution steps

y^{''} (t) + 16 y = 3 sin (5 t)

Solve linear ODE:

y = \frac{5}{12} sin (4 t) - \frac{1}{3} sin (5 t)

y = \frac{5}{12} sin (4 t) - \frac{1}{3} sin (5 t)

\frac{d}{d x} (\frac{1 - 6 x}{3 + x})

x \to 0 - lim (\frac{1}{2 x})

\int (1 - x)^{3} d x

\int_{0}^{1} (4 x) - (4 x) d x

\int \frac{1}{tan ( θ )} d θ

What is the solution for y^{''}+16y=3sin(5t),y(0)=0,y^'(0)=0 ?
The solution for y^{''}+16y=3sin(5t),y(0)=0,y^'(0)=0 is y= 5/12 sin(4t)-1/3 sin(5t)