MATH 204 PRACTICE MIDTERM III
Please work out each of
the given problems on your own paper.
Credit will be based on the steps that you show towards the final answer.
Show your work.
y'' + xy' + 2y = 0, y(0) = 0, y'(0) = 1
Determine the general solution of the differential equation that is valid in any interval not including the singular point.
x2y'' - xy' + y = 0
the following differential equation
y(0) = y'(0) = 0
the general solution of the given system of equations and describe the behavior
of the solution as
electric circuit is describes by the system of differential equations
Suppose that R = 1 ohm, C
= ½ farad, and L = 1 henry.
Find the general solution of the system in this case.
Find I(t) and V(t)
if I(0) = 2 amperes and V(0)
= 1 volt.
For the circuit of part A. determine the limiting values of I(t)
and V(t) as
Do these limiting values depend on the initial conditions?
answer the following true or false.
If true, explain why.
If false, explain why or provide a counter-example.
function that is not continuous at x = 2
, then the Laplace transform of f(x)
not continuous at x = 2
B. Let be a solution of the differential equation
x = -1 is in the interval of
convergence of y(x).