What is the solution for y^{''}+by=a ?

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

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y^{''}+by=a

y^{^{''}} + b y = a

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + y^{^{'}} + x = 0

y^{^{''}} + 2 y^{^{'}} + 2 y = e^{- x} cot (x) sec (x)

2 y^{^{''}} - 7 y^{^{'}} + 5 y = 11 - 7 x - 16 x^{2} + 5 x^{3}

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

y^{^{''}} + y^{^{'}} = 20

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