What is the solution for y^{''}+81y=cos(6t) ?

The solution for y^{''}+81y=cos(6t) is y=c_{1}cos(9t)+c_{2}sin(9t)+1/45 cos(6t)

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y^{''}+81y=cos(6t)

y^{^{''}} + 81 y = cos (6 t)

y = c_{1} cos (9 t) + c_{2} sin (9 t) + \frac{1}{45} cos (6 t)

Solution steps

y^{''} (t) + 81 y = cos (6 t)

Solve linear ODE:

y = c_{1} cos (9 t) + c_{2} sin (9 t) + \frac{1}{45} cos (6 t)

y = c_{1} cos (9 t) + c_{2} sin (9 t) + \frac{1}{45} cos (6 t)

t an g e n t f (x) = 5 x - 1, at x = 2

s l o p e in t erce pt (1.8) (0.5)

x \to 0 lim (\frac{2}{x ^{3} - x})

a re a y = 2 x^{3} - 13 x, y = x^{2} + 6

x \to 1 - lim (x)

What is the solution for y^{''}+81y=cos(6t) ?
The solution for y^{''}+81y=cos(6t) is y=c_{1}cos(9t)+c_{2}sin(9t)+1/45 cos(6t)