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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 2 y^{^{'}} - 3 y = - 20 sin (x)

y^{^{''}} - 2 y^{^{'}} + 3 y = 3 e^{2 t}

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

y^{^{''}} - 7 y^{^{'}} + 6 y = x, y^{1} (0) = e x

y^{^{''}} - 8 y^{^{'}} - 9 y = 10, y (0) = 0, y^{^{'}} (0) = 4

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