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

The solution for y^{''}-12y^'+36y=36x+2 is y=c_{1}e^{6x}+c_{2}xe^{6x}+x+7/18

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

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

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + x + \frac{7}{18}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + x + \frac{7}{18}

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + x + \frac{7}{18}

x^{^{''}} + 100 x^{^{'}} + 2500 x = 30

16 y^{^{''}} + 24 y^{^{'}} + 9 = 0

(D^{3} + D^{2} - 4 D - 4) y = 3 e^{- x} - 4 x - 6

y^{^{''}} + 2 y^{^{'}} + 5 y = 30 x^{3} + 2

y^{^{''}} + 4 y^{^{'}} + 5 y = 2 e^{x}

What is the solution for y^{''}-12y^'+36y=36x+2 ?
The solution for y^{''}-12y^'+36y=36x+2 is y=c_{1}e^{6x}+c_{2}xe^{6x}+x+7/18