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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

f (x) = e^{8 x}

arctan (x y)

\frac{d}{d x} (x^{3} + 7)

\int \frac{144 - x ^{2}}{x} d x

\frac{d}{d x} (3 x^{2} - 6 x + 9)

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