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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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