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

The solution for y^{''}+y=cos(ax) is y=c_{1}cos(x)+c_{2}sin(x)+(cos(ax))/(-a^2+1)

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

y^{^{''}} + y = cos (a x)

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

Solution steps

y^{''} (x) + y = cos (a x)

Solve linear ODE:

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

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

y^{^{''}} + 5 y^{^{'}} - 36 y = - 128 t + 72 t^{2}

y^{^{''}} + 4 y^{^{'}} - 32 y = - 112 t + 64 t^{2}

y^{^{''}} - 36.6 y^{^{'}} + 334.89 y = 18.5 u

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

y^{^{''}} + 3 y^{^{'}} - 4 y = e^{x} + x

What is the solution for y^{''}+y=cos(ax) ?
The solution for y^{''}+y=cos(ax) is y=c_{1}cos(x)+c_{2}sin(x)+(cos(ax))/(-a^2+1)