What is the solution for y^{''}+5y^'+6y=1,y(0)=1,y^'(0)=0 ?

The solution for y^{''}+5y^'+6y=1,y(0)=1,y^'(0)=0 is y=(5/3+5/6)e^{-2t}-5/3 e^{-3t}+1/6

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y^{''}+5y^'+6y=1,y(0)=1,y^'(0)=0

y^{^{''}} + 5 y^{^{'}} + 6 y = 1, y (0) = 1, y^{^{'}} (0) = 0

y = (\frac{5}{3} + \frac{5}{6}) e^{- 2 t} - \frac{5}{3} e^{- 3 t} + \frac{1}{6}

Solution steps

y^{''} (t) + 5 y^{'} (t) + 6 y = 1

Solve linear ODE:

y = (\frac{5}{3} + \frac{5}{6}) e^{- 2 t} - \frac{5}{3} e^{- 3 t} + \frac{1}{6}

y = (\frac{5}{3} + \frac{5}{6}) e^{- 2 t} - \frac{5}{3} e^{- 3 t} + \frac{1}{6}

What is the solution for y^{''}+5y^'+6y=1,y(0)=1,y^'(0)=0 ?
The solution for y^{''}+5y^'+6y=1,y(0)=1,y^'(0)=0 is y=(5/3+5/6)e^{-2t}-5/3 e^{-3t}+1/6