What is the solution for y^{''}+6y^'+5y=2e^x+10e^{5x} ?

The solution for y^{''}+6y^'+5y=2e^x+10e^{5x} is y=c_{1}e^{-x}+c_{2}e^{-5x}+(e^x+e^{5x})/6

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y^{''}+6y^'+5y=2e^x+10e^{5x}

y^{^{''}} + 6 y^{^{'}} + 5 y = 2 e^{x} + 10 e^{5 x}

y = c_{1} e^{- x} + c_{2} e^{- 5 x} + \frac{e ^{x} + e ^{5 x}}{6}

Solution steps

y^{''} (x) + 6 y^{'} (x) + 5 y = 2 e^{x} + 10 e^{5 x}

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 5 x} + \frac{e ^{x} + e ^{5 x}}{6}

y = c_{1} e^{- x} + c_{2} e^{- 5 x} + \frac{e ^{x} + e ^{5 x}}{6}

y^{^{''}} - 3 y^{^{'}} + 2 y = sin (x), y (0) = 1, y^{^{'}} (0) = 2

y^{^{''}} + 2 y^{^{'}} - 3 y = 5 sin (3 t)

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

y^{^{''}} + 6 y^{^{'}} + 13 y = 30 cos (x)

y^{^{''}} - 3 y^{^{'}} = 1

What is the solution for y^{''}+6y^'+5y=2e^x+10e^{5x} ?
The solution for y^{''}+6y^'+5y=2e^x+10e^{5x} is y=c_{1}e^{-x}+c_{2}e^{-5x}+(e^x+e^{5x})/6