What is the solution for y^{''}+7y^'+6y=e^{2t} ?

The solution for y^{''}+7y^'+6y=e^{2t} is y=c_{1}e^{-t}+c_{2}e^{-6t}+1/24 e^{2t}

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y^{''}+7y^'+6y=e^{2t}

y^{^{''}} + 7 y^{^{'}} + 6 y = e^{2 t}

y = c_{1} e^{- t} + c_{2} e^{- 6 t} + \frac{1}{24} e^{2 t}

Solution steps

y^{''} (t) + 7 y^{'} (t) + 6 y = e^{2 t}

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{- 6 t} + \frac{1}{24} e^{2 t}

y = c_{1} e^{- t} + c_{2} e^{- 6 t} + \frac{1}{24} e^{2 t}

y^{^{''}} + 4 y^{^{'}} + 4 y = 2 e^{- t}

y^{^{''}} - 2 y^{^{'}} + y = x + 1

y^{^{''}} + y = e^{- x} (2 sin (x) + 4 cos (x))

y^{^{''}} + y^{^{'}} - 7 y = 3 e^{2 x} - 2 e^{3 x}

y^{^{'''}} + y^{^{'}} - 10 = x e^{2 x}

What is the solution for y^{''}+7y^'+6y=e^{2t} ?
The solution for y^{''}+7y^'+6y=e^{2t} is y=c_{1}e^{-t}+c_{2}e^{-6t}+1/24 e^{2t}