What is the solution for y^{''}+7y^'+10y=7u ?

The solution for y^{''}+7y^'+10y=7u is y=c_{1}e^{-2t}+c_{2}e^{-5t}+(7u)/(10)

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y^{''}+7y^'+10y=7u

y^{^{''}} + 7 y^{^{'}} + 10 y = 7 u

y = c_{1} e^{- 2 t} + c_{2} e^{- 5 t} + \frac{7 u}{10}

Solution steps

y^{''} (t) + 7 y^{'} (t) + 10 y = 7 u

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} e^{- 5 t} + \frac{7 u}{10}

y = c_{1} e^{- 2 t} + c_{2} e^{- 5 t} + \frac{7 u}{10}

y^{^{''}} + 4 y = cos (x), y (0) = 0, y^{^{'}} (0) = 0

2 y^{^{''}} + y^{^{'}} = 3 x^{2} + 10 x

3 y^{^{''}} + 2 (9.81)^{2} y = 49 (9.81) cos (8 t)

y^{^{''}} + 2 y^{^{'}} + 5 y = 9 sin (2 t)

y^{^{''}} - 4 y^{^{'}} = 2 x - 1

What is the solution for y^{''}+7y^'+10y=7u ?
The solution for y^{''}+7y^'+10y=7u is y=c_{1}e^{-2t}+c_{2}e^{-5t}+(7u)/(10)