What is the solution for (d^2-d-12)*y=e^{3x} ?

The solution for (d^2-d-12)*y=e^{3x} is y=c_{1}e^{4x}+c_{2}e^{-3x}-1/6 e^{3x}

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(d^2-d-12)*y=e^{3x}

(d^{2} - d - 12) \cdot y = e^{3 x}

y = c_{1} e^{4 x} + c_{2} e^{- 3 x} - \frac{1}{6} e^{3 x}

Solution steps

(d^{2} - d - 12) y = e^{3 x}

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{- 3 x} - \frac{1}{6} e^{3 x}

y = c_{1} e^{4 x} + c_{2} e^{- 3 x} - \frac{1}{6} e^{3 x}

y^{^{''}} - y^{^{'}} = \frac{e ^{2} x}{( 2 + e ^{x} )}

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

d, d (t) = 4000 - 3000 e^{- 0.06 t}

(d^{2} - d - 2) \cdot y = 2 \cdot lo g_{10} (x) + \frac{1}{x} + \frac{1}{( x ^{2} )}

(d^{2} + 4 d + 3) y = e^{2} x

What is the solution for (d^2-d-12)*y=e^{3x} ?
The solution for (d^2-d-12)*y=e^{3x} is y=c_{1}e^{4x}+c_{2}e^{-3x}-1/6 e^{3x}