What is the solution for y^{''}+4y^'+5y=1,y(0)=0,y^'(0)=0 ?

The solution for y^{''}+4y^'+5y=1,y(0)=0,y^'(0)=0 is y=e^{-2t}(-1/5 cos(t)-2/5 sin(t))+1/5

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y^{''}+4y^'+5y=1,y(0)=0,y^'(0)=0

y^{^{''}} + 4 y^{^{'}} + 5 y = 1, y (0) = 0, y^{^{'}} (0) = 0

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

Solution steps

y^{''} (t) + 4 y^{'} (t) + 5 y = 1

Solve linear ODE:

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

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

What is the solution for y^{''}+4y^'+5y=1,y(0)=0,y^'(0)=0 ?
The solution for y^{''}+4y^'+5y=1,y(0)=0,y^'(0)=0 is y=e^{-2t}(-1/5 cos(t)-2/5 sin(t))+1/5