What is the solution for y^{''}+4y^'=6e^{-3t} ?

The solution for y^{''}+4y^'=6e^{-3t} is y=c_{1}+c_{2}e^{-4t}-2e^{-3t}

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y^{''}+4y^'=6e^{-3t}

y^{^{''}} + 4 y^{^{'}} = 6 e^{- 3 t}

y = c_{1} + c_{2} e^{- 4 t} - 2 e^{- 3 t}

Solution steps

y^{''} (t) + 4 y^{'} (t) = 6 e^{- 3 t}

Solve linear ODE:

y = c_{1} + c_{2} e^{- 4 t} - 2 e^{- 3 t}

y = c_{1} + c_{2} e^{- 4 t} - 2 e^{- 3 t}

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What is the solution for y^{''}+4y^'=6e^{-3t} ?
The solution for y^{''}+4y^'=6e^{-3t} is y=c_{1}+c_{2}e^{-4t}-2e^{-3t}