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

The solution for y^{''}+5y^'+4y=1,y(0)=0,y^'(0)=0 is y=(-1/12-1/4)e^{-t}+1/12 e^{-4t}+1/4

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

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

y = (- \frac{1}{12} - \frac{1}{4}) e^{- t} + \frac{1}{12} e^{- 4 t} + \frac{1}{4}

Solution steps

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

Solve linear ODE:

y = (- \frac{1}{12} - \frac{1}{4}) e^{- t} + \frac{1}{12} e^{- 4 t} + \frac{1}{4}

y = (- \frac{1}{12} - \frac{1}{4}) e^{- t} + \frac{1}{12} e^{- 4 t} + \frac{1}{4}

What is the solution for y^{''}+5y^'+4y=1,y(0)=0,y^'(0)=0 ?
The solution for y^{''}+5y^'+4y=1,y(0)=0,y^'(0)=0 is y=(-1/12-1/4)e^{-t}+1/12 e^{-4t}+1/4