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

The solution for y^{''}+y^'-6y=x+e^{2x} is y=c_{1}e^{2x}+c_{2}e^{-3x}-x/6-1/36+(e^{2x}x)/5

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

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

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - \frac{x}{6} - \frac{1}{36} + \frac{e ^{2 x} x}{5}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - \frac{x}{6} - \frac{1}{36} + \frac{e ^{2 x} x}{5}

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - \frac{x}{6} - \frac{1}{36} + \frac{e ^{2 x} x}{5}

y^{^{''}} + 12 y^{^{'}} + 100 y = 6

y^{^{''}} - 2 y^{^{'}} - 7 y = 3 x^{2}

1 y^{^{''}} + 4 y^{^{'}} + 4 y = \frac{e ^{- 2 x}}{x ^{2}}

y^{^{''}} + y^{^{'}} - 20 y = 3 e^{t}

y^{^{''}} - 4 y = 4 x - 4

What is the solution for y^{''}+y^'-6y=x+e^{2x} ?
The solution for y^{''}+y^'-6y=x+e^{2x} is y=c_{1}e^{2x}+c_{2}e^{-3x}-x/6-1/36+(e^{2x}x)/5