What is the solution for y^{''}-y^'-6y=(10x+7)e^{3x} ?

The solution for y^{''}-y^'-6y=(10x+7)e^{3x} is y=c_{1}e^{3x}+c_{2}e^{-2x}+e^{3x}x^2+e^{3x}x

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y^{''}-y^'-6y=(10x+7)e^{3x}

y^{^{''}} - y^{^{'}} - 6 y = (10 x + 7) e^{3 x}

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

Solution steps

y^{''} (x) - y^{'} (x) - 6 y = (10 x + 7) e^{3 x}

Solve linear ODE:

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

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

y^{^{''}} - 3 y^{^{'}} + 2 y = e^{4 t}

y^{^{''}} + 4 y^{^{'}} + 5 y = e^{- x} + 15 x

x^{^{''}} + 9.8 x = cos (2 t)

y^{^{''}} + 3 y^{^{'}} + 2 y = 3 sin (x) + 4 x

y^{^{''}} - 6 y^{^{'}} + 8 y = 2, y (0) = 0, y^{^{'}} (0) = 0

What is the solution for y^{''}-y^'-6y=(10x+7)e^{3x} ?
The solution for y^{''}-y^'-6y=(10x+7)e^{3x} is y=c_{1}e^{3x}+c_{2}e^{-2x}+e^{3x}x^2+e^{3x}x