What is the solution for y^{''}-y^'-6y=3e^{2x} ?

The solution for y^{''}-y^'-6y=3e^{2x} is y=c_{1}e^{3x}+c_{2}e^{-2x}-3/4 e^{2x}

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

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

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{3}{4} e^{2 x}

Solution steps

y^{''} (x) - y^{'} (x) - 6 y = 3 e^{2 x}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{3}{4} e^{2 x}

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{3}{4} e^{2 x}

x^{^{''}} + 25 x = cos (t)

y^{^{''}} + 7 y^{^{'}} - 12 y = e^{3} x - 2 e^{x} - 5 x

y^{^{''}} - 4 y = t cos (2 t)

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

\frac{d ^{2} y}{d x ^{2}} + 4 y = cos (\frac{9}{4} x)

What is the solution for y^{''}-y^'-6y=3e^{2x} ?
The solution for y^{''}-y^'-6y=3e^{2x} is y=c_{1}e^{3x}+c_{2}e^{-2x}-3/4 e^{2x}