What is the solution for x^{''}-9x-1=0 ?

The solution for x^{''}-9x-1=0 is x=c_{1}e^{3t}+c_{2}e^{-3t}-1/9

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x^{''}-9x-1=0

x^{^{''}} - 9 x - 1 = 0

x = c_{1} e^{3 t} + c_{2} e^{- 3 t} - \frac{1}{9}

Solution steps

x^{''} (t) - 9 x - 1 = 0

Solve linear ODE:

x = c_{1} e^{3 t} + c_{2} e^{- 3 t} - \frac{1}{9}

x = c_{1} e^{3 t} + c_{2} e^{- 3 t} - \frac{1}{9}

y^{^{''}} - y^{^{'}} = 1, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 9 y = cos (7 t)

(D^{2} + 3 D - 10) y = 20 + 5 e^{3 x}

(D^{4} + 4 D^{2}) y = sin (2 x) + x e^{x} + 4

y^{^{''}} + 5 \frac{d y}{d x} - 6 y = 2 + (- 2) sin (2 x)

What is the solution for x^{''}-9x-1=0 ?
The solution for x^{''}-9x-1=0 is x=c_{1}e^{3t}+c_{2}e^{-3t}-1/9