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

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

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y^{''}-y^'-2y=6e^{2t}

y^{^{''}} - y^{^{'}} - 2 y = 6 e^{2 t}

y = c_{1} e^{2 t} + c_{2} e^{- t} + 2 t e^{2 t}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- t} + 2 t e^{2 t}

y = c_{1} e^{2 t} + c_{2} e^{- t} + 2 t e^{2 t}

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