What is the solution for (d^2y)/(dx^2)-6(dy)/(dx)+9y=54x+18 ?

The solution for (d^2y)/(dx^2)-6(dy)/(dx)+9y=54x+18 is y=c_{1}e^{3x}+c_{2}xe^{3x}+6x+6

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(d^2y)/(dx^2)-6(dy)/(dx)+9y=54x+18

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 9 y = 54 x + 18

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 9 y = 54 x + 18

Solve linear ODE:

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

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

y^{^{'''}} - 6 y^{^{''}} + 12 y^{^{'}} - 8 y = 5 e^{2 x}

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

y^{^{''}} + y^{^{'}} = cos (\frac{t}{2})

y^{^{''}} - 4 y = t^{2} + 1

5 y^{^{''}} - 10 y^{^{'}} + 10 y = e x sec (x)

What is the solution for (d^2y)/(dx^2)-6(dy)/(dx)+9y=54x+18 ?
The solution for (d^2y)/(dx^2)-6(dy)/(dx)+9y=54x+18 is y=c_{1}e^{3x}+c_{2}xe^{3x}+6x+6