ENGR 213 Study Guide - Final Guide: Damping Ratio, University Of Manchester, Talking Lifestyle 1278
31 May 2018
School
Department
Course
Professor
Concordia University
Applied Ordinary Differential Equations, ENGR 213
Final Exam
20 April 2009
D. Korotkin, A. Stancu, S. Hashtrudi Zad
Evaluation out of 100. Only admissible calculators are allowed.
Time allotted: Three hours.
1. (15) (a) Find the general solution of the differential equation
dy
dx =2y+ 3
4x+ 52
.
You may leave the solution in implicit form.
(b) Solve the initial value problem
xdy
dx +y=ex, y(1) = 2
2. (10) Find the general solution (explicit or implicit) of the equation
(y2cos x−3x2y−2x)dx + (2ysin x−x3+ ln y)dy = 0 .
3. (10) Find the general solution of the equation using an appropriate substitution:
dy
dx = tan2(x+y).
You may leave the solution in implicit form.
4. (10) The Space Shuttle lands in Kennedy Space Center. The spacecraft touches down at t= 0
with a velocity of 100 m/sec. The spacecraft chute is deployed at t= 4 sec. Between touch down
and deployment of chute (0 ≤t≤4), the velocity of the spacecraft V(t) (in m/sec) is governed
by:
dV
dt = 0
and after the deployment of chute by:
dV
dt =−0.002V2
Determine when the spacecraft velocity reaches 20 m/sec.
5. (10) Find the general solution of the following differential equations using the method of unde-
termined coefficients.
(a) y′′ + 6y′+ 8y= sin 3x
(b) y′′ + 10y′+ 25y=ex
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