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

y^{^{''}} + 17 y^{^{'}} + 72 y = 4 x e^{x}

y^{^{''}} + 25 y = 4 sec (5 x)

\frac{d ^{2} v}{d x ^{2}} - k^{2} v = k^{2} n

y^{^{'''}} + 12 y^{^{''}} + 48 y^{^{'}} + 64 y = 9 e^{- 4 x}

y^{^{''}} + 3 y^{^{'}} + 2 y = 5 e^{- 2 x}

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