What is the solution for y^{''}+6y^'+5y=5x+1 ?

The solution for y^{''}+6y^'+5y=5x+1 is y=c_{1}e^{-x}+c_{2}e^{-5x}+x-1

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y^{''}+6y^'+5y=5x+1

y^{^{''}} + 6 y^{^{'}} + 5 y = 5 x + 1

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

Solution steps

y^{''} (x) + 6 y^{'} (x) + 5 y = 5 x + 1

Solve linear ODE:

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

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

What is the solution for y^{''}+6y^'+5y=5x+1 ?
The solution for y^{''}+6y^'+5y=5x+1 is y=c_{1}e^{-x}+c_{2}e^{-5x}+x-1