What is the solution for y^{''}+4y^'+5y=-15x+e^{-x} ?

The solution for y^{''}+4y^'+5y=-15x+e^{-x} is y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))-3x+12/5+1/2 e^{-x}

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

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

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) - 3 x + \frac{12}{5} + \frac{1}{2} e^{- x}

Solution steps

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

Solve linear ODE:

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) - 3 x + \frac{12}{5} + \frac{1}{2} e^{- x}

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) - 3 x + \frac{12}{5} + \frac{1}{2} e^{- x}

y^{^{''}} + 6 y^{^{'}} + 9 y = 5 e^{- 3 t}

4 y^{^{''}} - 4 y^{^{'}} + y = 24 e^{\frac{t}{2}}

y^{^{''''}} + 36 y^{^{''}} = sin (6 t) + t e^{7 t} + 4

y^{^{''}} + 8 y = 16 sin (x)

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

What is the solution for y^{''}+4y^'+5y=-15x+e^{-x} ?
The solution for y^{''}+4y^'+5y=-15x+e^{-x} is y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))-3x+12/5+1/2 e^{-x}