What is the solution for y^{''}+14y^'+49y=t^{-2}e^{-7t} ?

The solution for y^{''}+14y^'+49y=t^{-2}e^{-7t} is y=c_{1}e^{-7t}+c_{2}te^{-7t}-e^{-7t}ln(t)-e^{-7t}

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y^{''}+14y^'+49y=t^{-2}e^{-7t}

y^{^{''}} + 14 y^{^{'}} + 49 y = t^{- 2} e^{- 7 t}

y = c_{1} e^{- 7 t} + c_{2} t e^{- 7 t} - e^{- 7 t} ln (t) - e^{- 7 t}

Solution steps

y^{''} (t) + 14 y^{'} (t) + 49 y = t^{- 2} e^{- 7 t}

Solve linear ODE:

y = c_{1} e^{- 7 t} + c_{2} t e^{- 7 t} - e^{- 7 t} ln (t) - e^{- 7 t}

y = c_{1} e^{- 7 t} + c_{2} t e^{- 7 t} - e^{- 7 t} ln (t) - e^{- 7 t}

What is the solution for y^{''}+14y^'+49y=t^{-2}e^{-7t} ?
The solution for y^{''}+14y^'+49y=t^{-2}e^{-7t} is y=c_{1}e^{-7t}+c_{2}te^{-7t}-e^{-7t}ln(t)-e^{-7t}