What is the solution for y^{''}-9y^'+18y=9+18x ?

The solution for y^{''}-9y^'+18y=9+18x is y=c_{1}e^{6x}+c_{2}e^{3x}+x+1

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y^{''}-9y^'+18y=9+18x

y^{^{''}} - 9 y^{^{'}} + 18 y = 9 + 18 x

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

Solution steps

y^{''} (x) - 9 y^{'} (x) + 18 y = 9 + 18 x

Solve linear ODE:

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

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

y^{^{''}} + 2 y^{^{'}} - 3 y = 8 e^{- 3 x}

y^{^{''}} + 6 y^{^{'}} + 9 y = 3

y^{^{''}} - 16 y = 32 + 45 e^{x}, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + 25 y = 2 x cos (x)

y^{^{''}} + 4 y = sec^{3} (2 t)

What is the solution for y^{''}-9y^'+18y=9+18x ?
The solution for y^{''}-9y^'+18y=9+18x is y=c_{1}e^{6x}+c_{2}e^{3x}+x+1