What is the solution for y^{''}+7y^'+6y=30 ?

The solution for y^{''}+7y^'+6y=30 is y=c_{1}e^{-t}+c_{2}e^{-6t}+5

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y^{''}+7y^'+6y=30

y^{^{''}} + 7 y^{^{'}} + 6 y = 30

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

Solution steps

y^{''} (t) + 7 y^{'} (t) + 6 y = 30

Solve linear ODE:

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

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

y^{^{''}} - 4 y^{^{'}} + 13 y = sin (3 x)

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

y^{^{''}} + y^{^{'}} - 12 y = - sin (2 x) + 3 cos (2 x)

y^{^{''}} + 2 y^{^{'}} + y = e^{- t}, y (0) = 1, y^{^{'}} (0) = 3

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

What is the solution for y^{''}+7y^'+6y=30 ?
The solution for y^{''}+7y^'+6y=30 is y=c_{1}e^{-t}+c_{2}e^{-6t}+5