What is the solution for y^{''}-9y=e^{3x} ?

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

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y^{''}-9y=e^{3x}

y^{^{''}} - 9 y = e^{3 x}

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

Solution steps

y^{''} (x) - 9 y = e^{3 x}

Solve linear ODE:

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

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

f (x) = x^{\frac{2}{3}} (x^{2} - 4)

\frac{d}{d x} (4 x^{3} - x^{2} - 4 x + 3)

\frac{d}{d x} (y (θ, x) tan (θ))

y \frac{d y}{d x} - y^{3} = y^{2} ln (x)

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

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