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

The solution for x^{''}-9x^'-14x=0 is x=c_{1}e^{((9+sqrt(137))t)/2}+c_{2}e^{((9-sqrt(137))t)/2}

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

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

x = c_{1} e^{\frac{( 9 + 137 ) t}{2}} + c_{2} e^{\frac{( 9 - 137 ) t}{2}}

Solution steps

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

Solve linear ODE:

x = c_{1} e^{\frac{( 9 + 137 ) t}{2}} + c_{2} e^{\frac{( 9 - 137 ) t}{2}}

x = c_{1} e^{\frac{( 9 + 137 ) t}{2}} + c_{2} e^{\frac{( 9 - 137 ) t}{2}}

\frac{d ^{2} y}{d t ^{2}} + \frac{d y}{d t} = 0

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (- 1) = 2, y^{^{'}} (- 1) = 3

2 y^{^{''}} + 16 y^{^{'}} + 82 y = 0

y^{^{''''}} - y^{^{'''}} + y^{^{''}} = 0

121 y^{^{''}} + 198 y^{^{'}} + 80 y = 0

What is the solution for x^{''}-9x^'-14x=0 ?
The solution for x^{''}-9x^'-14x=0 is x=c_{1}e^{((9+sqrt(137))t)/2}+c_{2}e^{((9-sqrt(137))t)/2}