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

The solution for y^{''}+y^'-6y=e^{2t}+t is y=c_{1}e^{2t}+c_{2}e^{-3t}+(e^{2t}t)/5-t/6-1/36

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

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

y = c_{1} e^{2 t} + c_{2} e^{- 3 t} + \frac{e ^{2 t} t}{5} - \frac{t}{6} - \frac{1}{36}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- 3 t} + \frac{e ^{2 t} t}{5} - \frac{t}{6} - \frac{1}{36}

y = c_{1} e^{2 t} + c_{2} e^{- 3 t} + \frac{e ^{2 t} t}{5} - \frac{t}{6} - \frac{1}{36}

y^{^{'''}} - 3 y^{^{''}} - y^{^{'}} + 3 y = 1 + e^{x}

y^{^{''}} - y = 2 e^{- t}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 25 y = 6 sin (5 x)

2 y^{^{''}} + 3 y^{^{'}} - 2 y = 10 x^{2} - 4 x - 15

x^{^{'''}} + 10 x^{^{''}} + 33 x^{^{'}} + 36 x = 4 t e^{- 3 t}

What is the solution for y^{''}+y^'-6y=e^{2t}+t ?
The solution for y^{''}+y^'-6y=e^{2t}+t is y=c_{1}e^{2t}+c_{2}e^{-3t}+(e^{2t}t)/5-t/6-1/36