What is the solution for y^{''}+6y=cos(7t) ?

The solution for y^{''}+6y=cos(7t) is y=c_{1}cos(sqrt(6)t)+c_{2}sin(sqrt(6)t)-1/43 cos(7t)

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y^{''}+6y=cos(7t)

y^{^{''}} + 6 y = cos (7 t)

y = c_{1} cos (6 t) + c_{2} sin (6 t) - \frac{1}{43} cos (7 t)

Solution steps

y^{''} (t) + 6 y = cos (7 t)

Solve linear ODE:

y = c_{1} cos (6 t) + c_{2} sin (6 t) - \frac{1}{43} cos (7 t)

y = c_{1} cos (6 t) + c_{2} sin (6 t) - \frac{1}{43} cos (7 t)

(d^{2} + 144) (d^{2} - 144) 2 (d + 12) 4 x = 144

\frac{d ^{2} x}{d t ^{2}} + 36 x = 5 sin (4 t), x (0) = 0

y^{^{''}} - 2 y^{^{'}} - 3 y = x^{2}

x y^{^{'''}} - x y^{^{'}} = x^{4}

y^{^{''}} - y^{^{'}} = 5 e^{x}

What is the solution for y^{''}+6y=cos(7t) ?
The solution for y^{''}+6y=cos(7t) is y=c_{1}cos(sqrt(6)t)+c_{2}sin(sqrt(6)t)-1/43 cos(7t)