What is the solution for y^{''}-6y^'+8y=3+e^{-2t} ?

The solution for y^{''}-6y^'+8y=3+e^{-2t} is y=c_{1}e^{4t}+c_{2}e^{2t}+3/8+1/24 e^{-2t}

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y^{''}-6y^'+8y=3+e^{-2t}

y^{^{''}} - 6 y^{^{'}} + 8 y = 3 + e^{- 2 t}

y = c_{1} e^{4 t} + c_{2} e^{2 t} + \frac{3}{8} + \frac{1}{24} e^{- 2 t}

Solution steps

y^{''} (t) - 6 y^{'} (t) + 8 y = 3 + e^{- 2 t}

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2} e^{2 t} + \frac{3}{8} + \frac{1}{24} e^{- 2 t}

y = c_{1} e^{4 t} + c_{2} e^{2 t} + \frac{3}{8} + \frac{1}{24} e^{- 2 t}

What is the solution for y^{''}-6y^'+8y=3+e^{-2t} ?
The solution for y^{''}-6y^'+8y=3+e^{-2t} is y=c_{1}e^{4t}+c_{2}e^{2t}+3/8+1/24 e^{-2t}