- #1
Alphaboy2001
- 13
- 0
Homework Statement
Hi
I need to solve the following:
[itex]\frac{d^{2} x}{dt} + 2 b \frac{dx}{dt} + (b^2 - \frac{db}{dt}) x = 0[/tex]
2. The attempt at a solution
Isn't this equivalent to??::
[itex]x^{''} + 2bx^{'}+ (b^2 - b^{'})x = 0 \iff x^2 + 2x +1 = 0[/itex] If I let b = 1.
which gives me the solution [tex]\lamda = -1[/tex]
Thus giving me the particular solution
[tex]x(t) = c \cdot e^{-t}[/tex]
Have I understood correctly? There is no precondition regarding either t or b.
Best Regards
Alphaboy