What is the solution for y^{''}-12y^'+36y=36x+4 ?

The solution for y^{''}-12y^'+36y=36x+4 is y=c_{1}e^{6x}+c_{2}xe^{6x}+x+4/9

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y^{''}-12y^'+36y=36x+4

y^{^{''}} - 12 y^{^{'}} + 36 y = 36 x + 4

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + x + \frac{4}{9}

Solution steps

y^{''} (x) - 12 y^{'} (x) + 36 y = 36 x + 4

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + x + \frac{4}{9}

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + x + \frac{4}{9}

y^{^{''}} - 2 y^{^{'}} = 30 e^{- 3 t}, y (0) = 1, y^{^{'}} (0) = 0

2 y^{^{''}} + a y^{^{'}} + a y = e^{- 2 x} + x

y^{^{''}} + 2 y^{^{'}} + 2 y = 4 e^{- x} sec^{3} (x)

y^{^{''}} + 36 y = 36 sec^{2} (6 t)

y^{^{''}} - 3 y^{^{'}} = - 4 - 6 x

What is the solution for y^{''}-12y^'+36y=36x+4 ?
The solution for y^{''}-12y^'+36y=36x+4 is y=c_{1}e^{6x}+c_{2}xe^{6x}+x+4/9