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}

in v erse l a pl a ce \frac{1}{3 s + 1}

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

\frac{d}{d x} (9 + 9 - x)

\int (15 x + 2) d x

\int \frac{1}{4 y ^{2} + 1} d y

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}