What is the solution for y^{''}-5y^'+6y=(12x-7)e^{-x} ?

The solution for y^{''}-5y^'+6y=(12x-7)e^{-x} is y=c_{1}e^{3x}+c_{2}e^{2x}+e^{-x}x

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y^{''}-5y^'+6y=(12x-7)e^{-x}

y^{^{''}} - 5 y^{^{'}} + 6 y = (12 x - 7) e^{- x}

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

Solution steps

y^{''} (x) - 5 y^{'} (x) + 6 y = (12 x - 7) e^{- x}

Solve linear ODE:

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

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

y^{^{''}} + 25 y = 20 sin (5 x) + x cos (x)

2 y^{^{''}} - 13 y^{^{'}} + 20 y = 40 x^{2} + 8 x + 10

y^{^{''}} - 2 y^{^{'}} + 10 y = 20 x, y (0) = 0, y^{^{'}} (0) = 0

- a y^{^{''}} + b y - 1 = 0

y^{^{''}} + 16 y = 80 t^{2} - 96 t + 42, y (0) = 0, y^{^{'}} (0) = 14

What is the solution for y^{''}-5y^'+6y=(12x-7)e^{-x} ?
The solution for y^{''}-5y^'+6y=(12x-7)e^{-x} is y=c_{1}e^{3x}+c_{2}e^{2x}+e^{-x}x