What is the solution for -vy^{''}-ay=c ?

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

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-vy^{''}-ay=c

- v y^{^{''}} - a y = c

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

Solution steps

- v y^{''} (t) - a y (t) = c

Solve linear ODE:

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

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

y^{^{''}} - 7 y^{^{'}} + 10 y = e^{3 x} (- 1 + 10 x)

(d^{3} - 3 d - 2) y = 540 x^{3} e - x

y^{^{''}} - 9 y^{^{'}} + 18 y = e^{6 t}

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

y^{^{''}} + y^{^{'}} - 6 y = 2 e^{- 3 x} + e^{2 x}

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