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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 4 y^{^{'}} + 5 y = (x + 1)^{3}

y^{^{''}} + 9 y = 18 t, y (\frac{π}{2}) = 0

y^{^{''}} + 16 y = csc^{2} (4 t)

y^{^{''}} + 6 y^{^{'}} + 9 y = e^{- 3 x}

y^{^{''}} + 2 y^{^{'}} + 2 y = e^{- x} sec (x)

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