What is the solution for y^{''}-5y^'+6y=12x-4 ?

The solution for y^{''}-5y^'+6y=12x-4 is y=c_{1}e^{3x}+c_{2}e^{2x}+2x+1

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y^{''}-5y^'+6y=12x-4

y^{^{''}} - 5 y^{^{'}} + 6 y = 12 x - 4

y = c_{1} e^{3 x} + c_{2} e^{2 x} + 2 x + 1

Solution steps

y^{''} (x) - 5 y^{'} (x) + 6 y = 12 x - 4

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + 2 x + 1

y = c_{1} e^{3 x} + c_{2} e^{2 x} + 2 x + 1

y^{^{''}} - y = 4 e - x^{1} - e - 2 x

y^{^{''}} - 2 y^{^{'}} - 3 y = 12 e^{3 x}

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

y^{^{''}} + 40 y^{^{'}} + 625 y = 100 cos (10 t)

2 y^{^{''}} - y^{^{'}} - 2 y = 2 e^{- t}

What is the solution for y^{''}-5y^'+6y=12x-4 ?
The solution for y^{''}-5y^'+6y=12x-4 is y=c_{1}e^{3x}+c_{2}e^{2x}+2x+1