What is the solution for y^{''}-12y^'+36y=18x+2 ?

The solution for y^{''}-12y^'+36y=18x+2 is y=c_{1}e^{6x}+c_{2}xe^{6x}+x/2+2/9

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y^{''}-12y^'+36y=18x+2

y^{^{''}} - 12 y^{^{'}} + 36 y = 18 x + 2

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + \frac{x}{2} + \frac{2}{9}

Solution steps

y^{''} (x) - 12 y^{'} (x) + 36 y = 18 x + 2

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + \frac{x}{2} + \frac{2}{9}

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + \frac{x}{2} + \frac{2}{9}

y^{^{''}} - 5 y = 2 x^{3} - 4 x^{2} - x + 6

y^{^{''}} + 4 y^{^{'}} + 5 y = 10 e^{- 2 x} cos (x)

y^{^{''}} + 6 y^{^{'}} + 9 y = cos (x)

y^{^{''}} - 3 y^{^{'}} + 2 y = e^{3 x} cos (e^{x})

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

What is the solution for y^{''}-12y^'+36y=18x+2 ?
The solution for y^{''}-12y^'+36y=18x+2 is y=c_{1}e^{6x}+c_{2}xe^{6x}+x/2+2/9