What is the solution for y^{''}+5y=cos(7t) ?

The solution for y^{''}+5y=cos(7t) is y=c_{1}cos(sqrt(5)t)+c_{2}sin(sqrt(5)t)-1/44 cos(7t)

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y^{''}+5y=cos(7t)

y^{^{''}} + 5 y = cos (7 t)

y = c_{1} cos (5 t) + c_{2} sin (5 t) - \frac{1}{44} cos (7 t)

Solution steps

y^{''} (t) + 5 y = cos (7 t)

Solve linear ODE:

y = c_{1} cos (5 t) + c_{2} sin (5 t) - \frac{1}{44} cos (7 t)

y = c_{1} cos (5 t) + c_{2} sin (5 t) - \frac{1}{44} cos (7 t)

y^{^{''}} + 5 y^{^{'}} + 6 y = e^{- x} + sin (x)

y^{^{''}} + 2 y^{^{'}} = cos (4 x)

2 x^{^{''}} + 4 x + 20 x = 20 H (t)

2 y^{^{''}} - y^{^{'}} - y = 25 e^{- x}

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + 5 y = e^{x} sin (2 x)

What is the solution for y^{''}+5y=cos(7t) ?
The solution for y^{''}+5y=cos(7t) is y=c_{1}cos(sqrt(5)t)+c_{2}sin(sqrt(5)t)-1/44 cos(7t)