What is the solution for y^{''}+49y=cos(8t) ?

The solution for y^{''}+49y=cos(8t) is y=c_{1}cos(7t)+c_{2}sin(7t)-1/15 cos(8t)

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y^{''}+49y=cos(8t)

y^{^{''}} + 49 y = cos (8 t)

y = c_{1} cos (7 t) + c_{2} sin (7 t) - \frac{1}{15} cos (8 t)

Solution steps

y^{''} (t) + 49 y = cos (8 t)

Solve linear ODE:

y = c_{1} cos (7 t) + c_{2} sin (7 t) - \frac{1}{15} cos (8 t)

y = c_{1} cos (7 t) + c_{2} sin (7 t) - \frac{1}{15} cos (8 t)

x y^{^{'}} + y = 14 x

\int e^{3 x + 9} - 3 x^{2} d x

y^{^{''}} + 4 y = 8

\int 2 + cos (x) d x

x \to 2 lim (3 x^{2} - 7 x + 5)

What is the solution for y^{''}+49y=cos(8t) ?
The solution for y^{''}+49y=cos(8t) is y=c_{1}cos(7t)+c_{2}sin(7t)-1/15 cos(8t)