What is the solution for y^{'''}-7y^'+6y=e^{3x} ?

The solution for y^{'''}-7y^'+6y=e^{3x} is y=c_{1}e^x+c_{2}e^{2x}+c_{3}e^{-3x}+1/12 e^{3x}

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y^{'''}-7y^'+6y=e^{3x}

y^{^{'''}} - 7 y^{^{'}} + 6 y = e^{3 x}

y = c_{1} e^{x} + c_{2} e^{2 x} + c_{3} e^{- 3 x} + \frac{1}{12} e^{3 x}

Solution steps

y^{'''} (x) - 7 y^{'} (x) + 6 y = e^{3 x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{2 x} + c_{3} e^{- 3 x} + \frac{1}{12} e^{3 x}

y = c_{1} e^{x} + c_{2} e^{2 x} + c_{3} e^{- 3 x} + \frac{1}{12} e^{3 x}

\frac{d}{d x} (1 - x^{2} + y^{2})

\int \frac{x + 1}{3 x + 2} d x

\int_{- 3}^{1} x d x

x \to \infty lim (2 ln (x))

x \to - 6 lim (5 x^{2} + 6 x + a)

What is the solution for y^{'''}-7y^'+6y=e^{3x} ?
The solution for y^{'''}-7y^'+6y=e^{3x} is y=c_{1}e^x+c_{2}e^{2x}+c_{3}e^{-3x}+1/12 e^{3x}