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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 10 y^{^{'}} + 25 y = 4 - e^{t}, y (0) = 1, y (1) = 0

y^{^{''}} + y = 2 x^{2}

y^{^{''}} + 4 y^{^{'}} + 8 y = 4 e^{- 2 t} sin (2 t)

y^{^{''}} + 6 y^{^{'}} + 18 y = 180, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 4 y^{^{'}} + 40 y = 4 e^{- 2 t} cos (6 t)

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