What is the solution for y^{''}-6y+9=e^{3x} ?

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

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y^{''}-6y+9=e^{3x}

y^{^{''}} - 6 y + 9 = e^{3 x}

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

Solution steps

y^{''} (x) - 6 y + 9 = e^{3 x}

Solve linear ODE:

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

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

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