What is the solution for (d^2x)/(dt^2)+6(dx)/(dt)+3x=0 ?

The solution for (d^2x)/(dt^2)+6(dx)/(dt)+3x=0 is x=c_{1}e^{(-3+sqrt(6))t}+c_{2}e^{(-3-sqrt(6))t}

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(d^2x)/(dt^2)+6(dx)/(dt)+3x=0

\frac{d ^{2} x}{d t ^{2}} + 6 \frac{d x}{d t} + 3 x = 0

x = c_{1} e^{(- 3 + 6) t} + c_{2} e^{(- 3 - 6) t}

Solution steps

\frac{d ^{2} x}{d t ^{2}} + 6 \frac{d x}{d t} + 3 x = 0

Solve linear ODE:

x = c_{1} e^{(- 3 + 6) t} + c_{2} e^{(- 3 - 6) t}

x = c_{1} e^{(- 3 + 6) t} + c_{2} e^{(- 3 - 6) t}

What is the solution for (d^2x)/(dt^2)+6(dx)/(dt)+3x=0 ?
The solution for (d^2x)/(dt^2)+6(dx)/(dt)+3x=0 is x=c_{1}e^{(-3+sqrt(6))t}+c_{2}e^{(-3-sqrt(6))t}