What is the solution for y^{''}-2y-3y=3e^{2x} ?

The solution for y^{''}-2y-3y=3e^{2x} is y=c_{1}e^{sqrt(5)x}+c_{2}e^{-sqrt(5)x}-3e^{2x}

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y^{''}-2y-3y=3e^{2x}

y^{^{''}} - 2 y - 3 y = 3 e^{2 x}

y = c_{1} e^{5 x} + c_{2} e^{- 5 x} - 3 e^{2 x}

Solution steps

y^{''} (x) - 2 y - 3 y = 3 e^{2 x}

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{- 5 x} - 3 e^{2 x}

y = c_{1} e^{5 x} + c_{2} e^{- 5 x} - 3 e^{2 x}

y = x^{7 x}

t^{3} e^{- 3 t}

x \to 0 lim (6^{x})

\frac{\partial}{\partial x} (x^{3} y^{7})

- 5 t^{2} e^{- 4 t} + sin (3 t)

What is the solution for y^{''}-2y-3y=3e^{2x} ?
The solution for y^{''}-2y-3y=3e^{2x} is y=c_{1}e^{sqrt(5)x}+c_{2}e^{-sqrt(5)x}-3e^{2x}