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

The solution for y^{''}-5y^'+6y=6x+2-3e^{2x} is y=c_{1}e^{3x}+c_{2}e^{2x}+x+7/6+3xe^{2x}

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y^{''}-5y^'+6y=6x+2-3e^{2x}

y^{^{''}} - 5 y^{^{'}} + 6 y = 6 x + 2 - 3 e^{2 x}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + x + \frac{7}{6} + 3 x e^{2 x}

Solution steps

y^{''} (x) - 5 y^{'} (x) + 6 y = 6 x + 2 - 3 e^{2 x}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + x + \frac{7}{6} + 3 x e^{2 x}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + x + \frac{7}{6} + 3 x e^{2 x}

y^{^{'''}} - 4 y^{^{''}} + 6 y^{^{'}} - 4 y = x + e^{x} cos (x)

y^{^{''}} + 16 y = 9 sec (4 x)

y^{^{''}} - 3 y^{^{'}} + y = 8 x

2 t^{(4)} - y^{^{'''}} - 9 y^{^{''}} + 4 y^{^{'}} + 4 y = 0

y^{^{''}} + 6 y^{^{'}} + 5 y = 2 e^{x} + 10 e^{5 x}

What is the solution for y^{''}-5y^'+6y=6x+2-3e^{2x} ?
The solution for y^{''}-5y^'+6y=6x+2-3e^{2x} is y=c_{1}e^{3x}+c_{2}e^{2x}+x+7/6+3xe^{2x}