What is the solution for y^{''}+y^'+y=0.5 ?

The solution for y^{''}+y^'+y=0.5 is y=e^{-t/2}(c_{1}cos((sqrt(3)t)/2)+c_{2}sin((sqrt(3)t)/2))+0.5

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y^{''}+y^'+y=0.5

y^{^{''}} + y^{^{'}} + y = 0.5

y = e^{- \frac{t}{2}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2})) + 0.5

Solution steps

y^{''} (t) + y^{'} (t) + y = 0.5

Solve linear ODE:

y = e^{- \frac{t}{2}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2})) + 0.5

y = e^{- \frac{t}{2}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2})) + 0.5

f^{^{'}} (x) = 5

\frac{d}{d x} (\frac{( e ^{x} )}{ln ( x )})

cos (x), at x = \frac{π}{2}

\frac{d}{d r} (r 1 - r^{2})

x \to \infty lim (2 x - 1)

What is the solution for y^{''}+y^'+y=0.5 ?
The solution for y^{''}+y^'+y=0.5 is y=e^{-t/2}(c_{1}cos((sqrt(3)t)/2)+c_{2}sin((sqrt(3)t)/2))+0.5