What is the solution for (d^2-9)y=e^3x+e^{-3}x ?

The solution for (d^2-9)y=e^3x+e^{-3}x is y=c_{1}e^{3x}+c_{2}e^{-3x}-((e^6+1)x)/(9e^3)

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(d^2-9)y=e^3x+e^{-3}x

(d^{2} - 9) y = e^{3} x + e^{- 3} x

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{( e ^{6} + 1 ) x}{9 e ^{3}}

Solution steps

(d^{2} - 9) y = e^{3} x + e^{- 3} x

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{( e ^{6} + 1 ) x}{9 e ^{3}}

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{( e ^{6} + 1 ) x}{9 e ^{3}}

(d^{4} - 1) y = sin (x)

(d^{2} + 4 d - 12) y = (x - 1) e^{2} x

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

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

y^{^{''}} - 4 y^{^{'}} + 4 y = 12 e^{2 x} + x^{2}

What is the solution for (d^2-9)y=e^3x+e^{-3}x ?
The solution for (d^2-9)y=e^3x+e^{-3}x is y=c_{1}e^{3x}+c_{2}e^{-3x}-((e^6+1)x)/(9e^3)