What is the solution for y^{''}-12y^'+36y=42x+2 ?

The solution for y^{''}-12y^'+36y=42x+2 is y=c_{1}e^{6x}+c_{2}xe^{6x}+(7x)/6+4/9

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y^{''}-12y^'+36y=42x+2

y^{^{''}} - 12 y^{^{'}} + 36 y = 42 x + 2

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + \frac{7 x}{6} + \frac{4}{9}

Solution steps

y^{''} (x) - 12 y^{'} (x) + 36 y = 42 x + 2

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + \frac{7 x}{6} + \frac{4}{9}

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + \frac{7 x}{6} + \frac{4}{9}

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

y^{^{''}} + 2 y^{^{'}} - 3 y = e^{3 x} (2 + 8 x - 12 x^{2})

y^{^{''}} + 20 y^{^{'}} + 125 y = 9 sin (5 x)

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

y^{^{''}} + 6 y^{^{'}} + 9 y = \frac{1}{x}

What is the solution for y^{''}-12y^'+36y=42x+2 ?
The solution for y^{''}-12y^'+36y=42x+2 is y=c_{1}e^{6x}+c_{2}xe^{6x}+(7x)/6+4/9