Second-Order Homogeneous Differential Equations with Constant Coefficients
1. Write down a differential equation which models the motion of a spring.
2. Guess some of the solutions of y00
−y= 0 and check that your guess are correct?
3. Guess some of the solutions of y00
−4y= 0 and check that your guess are correct?
4. In this problem, we’ll look at the differential equation x00 + 3x0+ 2x= 0.
(a) Find all solutions of the differential equation of the form x(t) = ert. (There are two.)
(b) Let f(t) and g(t) be the solutions you found in (a). Show that C1f(t) + C2g(t) is also a solution
of x00 + 3x0+ 2x= 0.
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