What is the solution for (d^2y)/(dt^2)+2y=cos(7t) ?

The solution for (d^2y)/(dt^2)+2y=cos(7t) is y=c_{1}cos(sqrt(2)t)+c_{2}sin(sqrt(2)t)-1/47 cos(7t)

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(d^2y)/(dt^2)+2y=cos(7t)

\frac{d ^{2} y}{d t ^{2}} + 2 y = cos (7 t)

y = c_{1} cos (2 t) + c_{2} sin (2 t) - \frac{1}{47} cos (7 t)

Solution steps

\frac{d ^{2} y}{d t ^{2}} + 2 y = cos (7 t)

Solve linear ODE:

y = c_{1} cos (2 t) + c_{2} sin (2 t) - \frac{1}{47} cos (7 t)

y = c_{1} cos (2 t) + c_{2} sin (2 t) - \frac{1}{47} cos (7 t)

y^{^{''}} + 3 y = 2

y^{^{''}} - 2 y^{^{'}} - 3 y = 1, y (0) = 0, y^{^{'}} (0) = 0

a^{2} \cdot y + y^{^{''}} = cos (b \cdot t), y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - y^{^{'}} = 1 - x^{2}

y^{^{''}} - 4 y^{^{'}} + 4 y = 2 e^{x}

What is the solution for (d^2y)/(dt^2)+2y=cos(7t) ?
The solution for (d^2y)/(dt^2)+2y=cos(7t) is y=c_{1}cos(sqrt(2)t)+c_{2}sin(sqrt(2)t)-1/47 cos(7t)