What is the solution for y^{''}+6y^'+5y=-9e^{2x} ?

The solution for y^{''}+6y^'+5y=-9e^{2x} is y=c_{1}e^{-x}+c_{2}e^{-5x}-3/7 e^{2x}

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y^{''}+6y^'+5y=-9e^{2x}

y^{^{''}} + 6 y^{^{'}} + 5 y = - 9 e^{2 x}

y = c_{1} e^{- x} + c_{2} e^{- 5 x} - \frac{3}{7} e^{2 x}

Solution steps

y^{''} (x) + 6 y^{'} (x) + 5 y = - 9 e^{2 x}

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 5 x} - \frac{3}{7} e^{2 x}

y = c_{1} e^{- x} + c_{2} e^{- 5 x} - \frac{3}{7} e^{2 x}

y^{^{''}} + 18 y^{^{'}} + 81 y = x, y (0) = 0, y^{^{'}} (0) = 0

20 y^{^{''}} + 9 y^{^{'}} + x = 0, y (0) = 0, y^{^{'}} (0) = 3

d, d (x) = \frac{2 x ^{3} + 1}{x ^{6}}

y^{^{''}} + 9 y = 18 cos (3 x)

y^{^{''}} - 2 y^{^{'}} + y = 4 cos (3 x) - 2 sin (2 x)

What is the solution for y^{''}+6y^'+5y=-9e^{2x} ?
The solution for y^{''}+6y^'+5y=-9e^{2x} is y=c_{1}e^{-x}+c_{2}e^{-5x}-3/7 e^{2x}