What is the solution for y^{''}-12y^'+36y=12x+6 ?

The solution for y^{''}-12y^'+36y=12x+6 is y=c_{1}e^{6x}+c_{2}xe^{6x}+x/3+5/18

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y^{''}-12y^'+36y=12x+6

y^{^{''}} - 12 y^{^{'}} + 36 y = 12 x + 6

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + \frac{x}{3} + \frac{5}{18}

Solution steps

y^{''} (x) - 12 y^{'} (x) + 36 y = 12 x + 6

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + \frac{x}{3} + \frac{5}{18}

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + \frac{x}{3} + \frac{5}{18}

What is the solution for y^{''}-12y^'+36y=12x+6 ?
The solution for y^{''}-12y^'+36y=12x+6 is y=c_{1}e^{6x}+c_{2}xe^{6x}+x/3+5/18