What is the solution for y^{''}+12y^'+36y=t^{-2}e^{-6t} ?

The solution for y^{''}+12y^'+36y=t^{-2}e^{-6t} is y=c_{1}e^{-6t}+c_{2}te^{-6t}-e^{-6t}ln(t)-e^{-6t}

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y^{''}+12y^'+36y=t^{-2}e^{-6t}

y^{^{''}} + 12 y^{^{'}} + 36 y = t^{- 2} e^{- 6 t}

y = c_{1} e^{- 6 t} + c_{2} t e^{- 6 t} - e^{- 6 t} ln (t) - e^{- 6 t}

Solution steps

y^{''} (t) + 12 y^{'} (t) + 36 y = t^{- 2} e^{- 6 t}

Solve linear ODE:

y = c_{1} e^{- 6 t} + c_{2} t e^{- 6 t} - e^{- 6 t} ln (t) - e^{- 6 t}

y = c_{1} e^{- 6 t} + c_{2} t e^{- 6 t} - e^{- 6 t} ln (t) - e^{- 6 t}

y^{^{''}} - 2 y^{^{'}} + 2 y = 0

y = 4 - x^{2}, (- 1, 3)

\frac{1}{3 s + 1}

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

\int (z + 2)^{2} d z

What is the solution for y^{''}+12y^'+36y=t^{-2}e^{-6t} ?
The solution for y^{''}+12y^'+36y=t^{-2}e^{-6t} is y=c_{1}e^{-6t}+c_{2}te^{-6t}-e^{-6t}ln(t)-e^{-6t}