What is the solution for (d^2y)/(dx^2)-6(dy)/(dx)+9y=9x ?

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

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(d^2y)/(dx^2)-6(dy)/(dx)+9y=9x

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 9 y = 9 x

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 9 y = 9 x

Solve linear ODE:

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

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

y^{^{''}} + 9 y^{^{'}} + 22 y = e^{- 3 x}

(D^{2} - 4 D + 5) y = (x + 1)^{3}

d, d (t) = \frac{1}{2} t^{2} - 10 t

y^{^{''}} - 2 y^{^{'}} + y = 4 x^{2} - 7 + x^{- 1} e^{x}

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} + y = e^{x}

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