What is the solution for x^{''}+15x^'+24x=0 ?

The solution for x^{''}+15x^'+24x=0 is x=c_{1}e^{((-15+sqrt(129))t)/2}+c_{2}e^{((-15-sqrt(129))t)/2}

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x^{''}+15x^'+24x=0

x^{^{''}} + 15 x^{^{'}} + 24 x = 0

x = c_{1} e^{\frac{( - 15 + 129 ) t}{2}} + c_{2} e^{\frac{( - 15 - 129 ) t}{2}}

Solution steps

x^{''} (t) + 15 x^{'} (t) + 24 x = 0

Solve linear ODE:

x = c_{1} e^{\frac{( - 15 + 129 ) t}{2}} + c_{2} e^{\frac{( - 15 - 129 ) t}{2}}

x = c_{1} e^{\frac{( - 15 + 129 ) t}{2}} + c_{2} e^{\frac{( - 15 - 129 ) t}{2}}

What is the solution for x^{''}+15x^'+24x=0 ?
The solution for x^{''}+15x^'+24x=0 is x=c_{1}e^{((-15+sqrt(129))t)/2}+c_{2}e^{((-15-sqrt(129))t)/2}