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

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

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

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

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + 3 x^{2} e^{3 x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + 3 x^{2} e^{3 x}

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + 3 x^{2} e^{3 x}

\int cos (\frac{x}{2}) d x

x \to 3 lim (4 cos (x))

x, x^{0.5}

x \to 1 - lim (\frac{( 1 )}{x - 1})

e^{x}, e^{- x}, - 1, 1

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