What is the solution for x^{''}-9x^'-14=0 ?

The solution for x^{''}-9x^'-14=0 is x=c_{1}e^{9t}+c_{2}-(14t)/9

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x^{''}-9x^'-14=0

x^{^{''}} - 9 x^{^{'}} - 14 = 0

x = c_{1} e^{9 t} + c_{2} - \frac{14 t}{9}

Solution steps

x^{''} (t) - 9 x^{'} (t) - 14 = 0

Solve linear ODE:

x = c_{1} e^{9 t} + c_{2} - \frac{14 t}{9}

x = c_{1} e^{9 t} + c_{2} - \frac{14 t}{9}

x^{^{''}} - 10 x^{^{'}} + 25 x = 78 t^{2} e^{5 t}

y^{^{''}} + 2 y^{^{'}} + y = 1, y (0) = 2, y^{^{'}} (0) = 1

y^{^{''}} + 4 y^{^{'}} + 4 y = 6 e^{-} 2 x - 8 sin (x) + 6 cos (x)

y^{^{''}} - 4 y = e^{3 x}

y^{^{''}} - 9 y^{^{'}} + 20 y = 3 x + e^{4 x}

What is the solution for x^{''}-9x^'-14=0 ?
The solution for x^{''}-9x^'-14=0 is x=c_{1}e^{9t}+c_{2}-(14t)/9