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

The solution for y^{''}-4y^'=6e^{3t}-3e^{-t} is y=c_{1}e^{4t}+c_{2}-2e^{3t}-3/5 e^{-t}

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

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

y = c_{1} e^{4 t} + c_{2} - 2 e^{3 t} - \frac{3}{5} e^{- t}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2} - 2 e^{3 t} - \frac{3}{5} e^{- t}

y = c_{1} e^{4 t} + c_{2} - 2 e^{3 t} - \frac{3}{5} e^{- t}

y^{^{''}} + 2 y^{^{'}} - 24 y = 16 - (x + 2) e^{4 x}

y^{^{'''}} + y^{^{''}} = e^{x} cos (x)

2 y^{^{''}} + 18 y = 6 tan (3 x)

y^{^{''}} + a y^{^{'}} = b

y^{^{''}} - 8 y^{^{'}} + 16 y = 10 e^{4 x} sec (x)

What is the solution for y^{''}-4y^'=6e^{3t}-3e^{-t} ?
The solution for y^{''}-4y^'=6e^{3t}-3e^{-t} is y=c_{1}e^{4t}+c_{2}-2e^{3t}-3/5 e^{-t}