What is the solution for (d^2x)/(dt^2)-4(dx)/(dt)+5x=0 ?

The solution for (d^2x)/(dt^2)-4(dx)/(dt)+5x=0 is x=e^{2t}(c_{1}cos(t)+c_{2}sin(t))

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(d^2x)/(dt^2)-4(dx)/(dt)+5x=0

\frac{d ^{2} x}{d t ^{2}} - 4 \frac{d x}{d t} + 5 x = 0

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

Solution steps

\frac{d ^{2} x}{d t ^{2}} - 4 \frac{d x}{d t} + 5 x = 0

Solve linear ODE:

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

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

y^{^{''}} - 4 y^{^{'}} + 5 y = 0, y^{1} (0) = e^{x} cos (2 x)

4 y^{^{''}} + 24 y^{^{'}} + 37 y = 0, y (π) = 1

y^{^{'''}} - 3 y^{^{''}} - 5 y^{^{'}} + 39 y = 0

y^{^{''}} + 29.4 y = 0

y^{^{''}} + 2 y^{^{'}} + 5 y = 0, y (0) = 1, y^{^{'}} (0) = 0

What is the solution for (d^2x)/(dt^2)-4(dx)/(dt)+5x=0 ?
The solution for (d^2x)/(dt^2)-4(dx)/(dt)+5x=0 is x=e^{2t}(c_{1}cos(t)+c_{2}sin(t))