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

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

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y^{''}+y^'+y=5x+3

y^{^{''}} + y^{^{'}} + y = 5 x + 3

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

Solution steps

y^{''} (x) + y^{'} (x) + y = 5 x + 3

Solve linear ODE:

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

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

y^{^{''}} + 5 y^{^{'}} + 6 y = 3 e^{- 2 t}

y^{^{'''}} - 2 y^{^{''}} - 21 y^{^{'}} - 18 y = 3 + 4 e^{- t}

y^{^{''}} + 9 y = 18 t, y (\frac{π}{2}) = 0, y (0) = 0

y^{^{''}} + 4 y^{^{'}} + 4 y = x^{- 2} e^{- 2 x}

y^{^{''}} + 16 y = sin (5 x)

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