What is the solution for ay^{''}+by=c ?

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

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ay^{''}+by=c

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 2 y^{^{'}} + 37 y = 4 H (t)

5 y^{^{''}} + 4 y^{^{'}} + 8 y = 4 x - 1

4 y^{^{''}} + 20 y^{^{'}} + 169 y = e^{2 t}

(D^{3} + 8) y = x^{4} + 2 x + 1

y^{^{''}} - 6 y^{^{'}} + 13 y = 13

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