What is the solution for x^{''}-2x^'-x=0 ?

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

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x^{''}-2x^'-x=0

x^{^{''}} - 2 x^{^{'}} - x = 0

x = c_{1} e^{(1 + 2) t} + c_{2} e^{(1 - 2) t}

Solution steps

x^{''} (t) - 2 x^{'} (t) - x = 0

Solve linear ODE:

x = c_{1} e^{(1 + 2) t} + c_{2} e^{(1 - 2) t}

x = c_{1} e^{(1 + 2) t} + c_{2} e^{(1 - 2) t}

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