What is the solution for y^{''}+6y^'+10y=5x-2 ?

The solution for y^{''}+6y^'+10y=5x-2 is y=e^{-3x}(c_{1}cos(x)+c_{2}sin(x))+x/2-1/2

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y^{''}+6y^'+10y=5x-2

y^{^{''}} + 6 y^{^{'}} + 10 y = 5 x - 2

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

Solution steps

y^{''} (x) + 6 y^{'} (x) + 10 y = 5 x - 2

Solve linear ODE:

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

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

\frac{d}{d θ} (1 + cos (θ))

\frac{d}{d x} (cos (x))

x \frac{d y}{d x} - 2 y = x y^{3}

\int t^{2} - 4 t + 8 d t

t \to 2 - lim (\frac{t + 2}{t ^{2} - 4})

What is the solution for y^{''}+6y^'+10y=5x-2 ?
The solution for y^{''}+6y^'+10y=5x-2 is y=e^{-3x}(c_{1}cos(x)+c_{2}sin(x))+x/2-1/2