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

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

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

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

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{5 x}{6} - \frac{5}{36}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{5 x}{6} - \frac{5}{36}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{5 x}{6} - \frac{5}{36}

y^{^{''}} - 2 y^{^{'}} - 3 y = 6 t e^{2 t}, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + y = t - 3 sin (2 t), y (0) = 1, y^{^{'}} (0) = - 3

y^{^{''''}} - y = t e^{t} + sin (t)

y^{^{''}} + 81 y = 8 sin (9 t)

x^{^{''}} + 2 x^{^{'}} + 5 x = 5 cos (t)

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