What is the solution for y^{''}-4y=6e^t ?

The solution for y^{''}-4y=6e^t is y=c_{1}e^{2t}+c_{2}e^{-2t}-2e^t

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y^{''}-4y=6e^t

y^{^{''}} - 4 y = 6 e^{t}

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

Solution steps

y^{''} (t) - 4 y = 6 e^{t}

Solve linear ODE:

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

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

5 cos (2 x), 5 - 5 cos (2 x), 0, \frac{π}{2}

\int \frac{20 x ^{3}}{4 + 5 x ^{4}} d x

y^{^{''}} + 4 y = t \cdot sin (2 t)

2 + 5 arctan (\frac{x}{2})

\frac{1}{( x + 6 ) ^{2}}

What is the solution for y^{''}-4y=6e^t ?
The solution for y^{''}-4y=6e^t is y=c_{1}e^{2t}+c_{2}e^{-2t}-2e^t