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

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

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y^{''}+y^'-6y=3e^{2t}

y^{^{''}} + y^{^{'}} - 6 y = 3 e^{2 t}

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

Solution steps

y^{''} (t) + y^{'} (t) - 6 y = 3 e^{2 t}

Solve linear ODE:

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

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

y^{^{''}} - 4 y = 6 x - 4 x^{3}

y^{^{'''}} - y^{^{''}} + 4 y^{^{'}} - 4 y = - 3 e^{t} + 4 e^{2 t}

y^{^{''}} - 8 y^{^{'}} + 16 y = 8 + 16 x

y^{^{''}} + y = 2 x \cdot sin (x)

2 y^{^{''}} - 4 y^{^{'}} + 3 y = 2 e^{3 x} - 6

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