What is the solution for 10y^{''}+1000y=20cos(8t),y(0)=0,y^'(0)=0 ?

The solution for 10y^{''}+1000y=20cos(8t),y(0)=0,y^'(0)=0 is y= 1/18 cos(8t)-1/18 cos(10t)

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10y^{''}+1000y=20cos(8t),y(0)=0,y^'(0)=0

10 y^{^{''}} + 1000 y = 20 cos (8 t), y (0) = 0, y^{^{'}} (0) = 0

y = \frac{1}{18} cos (8 t) - \frac{1}{18} cos (10 t)

Solution steps

10 y^{''} (t) + 1000 y = 20 cos (8 t)

Solve linear ODE:

y = \frac{1}{18} cos (8 t) - \frac{1}{18} cos (10 t)

y = \frac{1}{18} cos (8 t) - \frac{1}{18} cos (10 t)

y = 3 x - 2

y^{^{''}} + 6 y^{^{'}} + 34 y = 0

x \to 0 lim (\frac{5 x ^{3}}{x})

\frac{1}{4} x^{2}, 2 x^{2}, x - 3

\frac{\partial}{\partial x} (6 x (x^{2} + y^{2} + z^{2})^{2})

What is the solution for 10y^{''}+1000y=20cos(8t),y(0)=0,y^'(0)=0 ?
The solution for 10y^{''}+1000y=20cos(8t),y(0)=0,y^'(0)=0 is y= 1/18 cos(8t)-1/18 cos(10t)