What is the solution for y^{''}-5y^'+6y=-2x+1 ?

The solution for y^{''}-5y^'+6y=-2x+1 is y=c_{1}e^{3x}+c_{2}e^{2x}-x/3-1/9

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y^{''}-5y^'+6y=-2x+1

y^{^{''}} - 5 y^{^{'}} + 6 y = - 2 x + 1

y = c_{1} e^{3 x} + c_{2} e^{2 x} - \frac{x}{3} - \frac{1}{9}

Solution steps

y^{''} (x) - 5 y^{'} (x) + 6 y = - 2 x + 1

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} - \frac{x}{3} - \frac{1}{9}

y = c_{1} e^{3 x} + c_{2} e^{2 x} - \frac{x}{3} - \frac{1}{9}

0.05 y^{^{''}} + 5 y^{^{'}} + \frac{1}{0.006} y = 5 sin (25 x)

(d^{2} - d) y = e^{x} cos (x)

y^{^{''}} + 17 y^{^{'}} + 30 y = cos (2 t)

e^{x} y^{^{''}} + 2 e^{x} y^{^{'}} + 5 e^{x} y = sin (2 x)

y^{^{'''}} - 13 y^{^{''}} + 36 y^{^{'}} = 72 e^{x}

What is the solution for y^{''}-5y^'+6y=-2x+1 ?
The solution for y^{''}-5y^'+6y=-2x+1 is y=c_{1}e^{3x}+c_{2}e^{2x}-x/3-1/9