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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 e^{x} - 9 + 24 x + 4

y^{^{''''}} - 2 y^{^{''}} + 1 = 0

x^{^{''}} + b \cdot x^{^{'}} + a = 0

x^{^{''}} - 6 x - 16 x = sin (2 t)

y^{^{''}} + 4 y = x^{2} + 5 e^{x}

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