What is the solution for y^{''}+y=cos(at) ?

The solution for y^{''}+y=cos(at) is y=c_{1}cos(t)+c_{2}sin(t)+(cos(at))/(-a^2+1)

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y^{''}+y=cos(at)

y^{^{''}} + y = cos (a t)

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

Solution steps

y^{''} (t) + y = cos (a t)

Solve linear ODE:

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

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

y^{^{'''}} - 2 y^{^{''}} - y^{^{'}} + 2 y = - 8 e^{x} + 6 e^{- x}

y^{^{''}} + 2 y^{^{'}} + y = 6 e^{- t}, y (0) = y

y^{^{''}} + 2 y^{^{'}} + y = e^{- x} \cdot ln (x)

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

y^{^{''}} + 4 y + 5 = 0

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