What is the solution for (d^2x)/(dt^2)-6(dx)/(dt)+9x=0 ?

The solution for (d^2x)/(dt^2)-6(dx)/(dt)+9x=0 is x=c_{1}e^{3t}+c_{2}te^{3t}

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(d^2x)/(dt^2)-6(dx)/(dt)+9x=0

\frac{d ^{2} x}{d t ^{2}} - 6 \frac{d x}{d t} + 9 x = 0

x = c_{1} e^{3 t} + c_{2} t e^{3 t}

Solution steps

\frac{d ^{2} x}{d t ^{2}} - 6 \frac{d x}{d t} + 9 x = 0

Solve linear ODE:

x = c_{1} e^{3 t} + c_{2} t e^{3 t}

x = c_{1} e^{3 t} + c_{2} t e^{3 t}

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

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y^{^{'}} (- 1) = 9, y (- 1) = 3

y^{^{'''}} - 2 y^{^{''}} - 9 y^{^{'}} + 4 y = 0

y^{^{''}} + a y = 0, y (0) = 0, y (1) = 0

(D^{3} + D^{2} + D + 1) y = 0

What is the solution for (d^2x)/(dt^2)-6(dx)/(dt)+9x=0 ?
The solution for (d^2x)/(dt^2)-6(dx)/(dt)+9x=0 is x=c_{1}e^{3t}+c_{2}te^{3t}