204 PRACTICE MIDTERM II
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.
Solve the following differential equations.
A. y'' - 2y' + 2y = 0, y(0) = 0, y'(0) = 5
B. y''' - 3y'' + 3y' - y = 0
y''' - y' = e2t + e3t
Solve this differential equation using the method of UC functions .
Solve this differential equation using the method of variation of
A 2 kg mass
stretches a spring 0.0784 meters. The
mass is attached to a viscous damper that exerts a force of 4N when the velocity
is 0.1 m/sec. The mass is then
pulled down 0.5m and released.
Determine the equation of motion for this system.
Describe (qualitatively) the difference between replacing the viscous
damper with an external force of F
and replacing the damper with an external force of F
answer the following true or false. If
false, explain why or provide a counter-example.
If true, explain why.
A. The differential equation
(t - 1)y'' + cos t y' + (t - 1)y = et, y(0) = 3, y'(0) = 4
has a unique
solution defined for all real numbers.
B. Let y1 = t + 1, y2 = 4t, be solutions of the differential equation
y''' + p(t)y'' + q(t)y' + r(t)y = s(t)
with p, q, r, and s all continuous. Then
y3 = sin t
be a solution of this differential equation.
mu'' + gu' + ku
LQ'' + RQ' + 1/C Q = E'(t)