What is the solution for y^{''}+y^'+y=k ?

The solution for y^{''}+y^'+y=k is y=e^{-t/2}(c_{1}cos((sqrt(3)t)/2)+c_{2}sin((sqrt(3)t)/2))+k

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y^{''}+y^'+y=k

y^{^{''}} + y^{^{'}} + y = k

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

Solution steps

y^{''} (t) + y^{'} (t) + y = k

Solve linear ODE:

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

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

What is the solution for y^{''}+y^'+y=k ?
The solution for y^{''}+y^'+y=k is y=e^{-t/2}(c_{1}cos((sqrt(3)t)/2)+c_{2}sin((sqrt(3)t)/2))+k