What is the solution for x^{''}-6x^{''}+x=0 ?

The solution for x^{''}-6x^{''}+x=0 is x=c_{1}e^{t/(sqrt(5))}+c_{2}e^{-t/(sqrt(5))}

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x^{''}-6x^{''}+x=0

x^{^{''}} - 6 x^{^{''}} + x = 0

x = c_{1} e^{\frac{t}{5}} + c_{2} e^{- \frac{t}{5}}

Solution steps

x^{''} (t) - 6 x^{''} (t) + x = 0

Solve linear ODE:

x = c_{1} e^{\frac{t}{5}} + c_{2} e^{- \frac{t}{5}}

x = c_{1} e^{\frac{t}{5}} + c_{2} e^{- \frac{t}{5}}

y^{^{'''}} + 9 y^{^{'}} = 0, y (0) = 5, y^{^{'}} (0) = 4, y^{^{''}} (0) = 3

y^{^{''}} - \frac{2}{5} y = 0

y^{^{''''}} + 2 y^{^{'''}} - 4 y^{^{''}} - 2 y^{^{'}} + \frac{1}{2} y = 0

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

12 x^{^{''}} + 6 x^{^{'}} + 18 x = 0

What is the solution for x^{''}-6x^{''}+x=0 ?
The solution for x^{''}-6x^{''}+x=0 is x=c_{1}e^{t/(sqrt(5))}+c_{2}e^{-t/(sqrt(5))}