What is the solution for y^{''}+6y^'+5y=30 ?

The solution for y^{''}+6y^'+5y=30 is y=c_{1}e^{-t}+c_{2}e^{-5t}+6

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y^{''}+6y^'+5y=30

y^{^{''}} + 6 y^{^{'}} + 5 y = 30

y = c_{1} e^{- t} + c_{2} e^{- 5 t} + 6

Solution steps

y^{''} (t) + 6 y^{'} (t) + 5 y = 30

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{- 5 t} + 6

y = c_{1} e^{- t} + c_{2} e^{- 5 t} + 6

4 y^{^{''}} - 4 y^{^{'}} + y = 80 e^{\frac{t}{2}}

- 2 y^{^{''}} + y = e^{- 0.2 x}, y (0) = 1, y^{^{'}} (1) = - y (1)

y^{^{''}} - 9 y = 9 x e^{- 3 x}

y^{^{'''}} - 2 y^{^{''}} + y^{^{'}} = x e^{x} + 5

y^{^{''}} - 64 y = sinh (8 x)

What is the solution for y^{''}+6y^'+5y=30 ?
The solution for y^{''}+6y^'+5y=30 is y=c_{1}e^{-t}+c_{2}e^{-5t}+6