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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{1}{6} y^{^{''}} + 6 y = 3 tan (6 t) - \frac{1}{3} e^{t}

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

y^{^{''}} + 5 y^{^{'}} + 6 y = e^{2 t}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 2 y^{^{'}} - 3 y = e^{4} x

y^{^{''''}} - 2 y^{^{''}} + y = 11 t + 8

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