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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

x \to 3 lim (x 25 - x^{3})

\frac{d}{d x} (3 - 2 sin (2 x - \frac{π}{4}))

\int e^{x} 3 x^{2} d x

x^{2} \frac{d ^{2} y}{d x ^{2}} - 5 x \frac{d y}{d x} + 9 y = 0

\int \frac{( x ^{2} - x + 30 )}{x ^{3} + 5 x} d x

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