EGR 265, TEST I 1
EGR 265, Math Tools for Engineering Problem Solving
September 12, 2012, 50 minutes
TEST I
Name: ..........................................
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Total
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Unique Solution - Math Tools for Engineering - Exam, Exams of Mathematics
Key points of this exam paper are : Unique Solution, Linear Order, Differential Equation, Initial Condition, Non-Linear Order, Direction Field, Two Solution Curves, Newton's Law of Cooling, Unknown Warming Rate, Describe Warming Processes
Typology: Exams
2012/2013
1 / 6
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EGR 265, Math Tools for Engineering Problem Solving
September 12, 2012, 50 minutes
TEST I
Name:..........................................
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Total
Problem 1 (16 Points)
Determine the order of the following ODEs. Also, state if they are linear or non-linear. (4P+4P+4P+4P)
(a) 2y′y = cos x
(b) y^4 − xy′′′^ = y′^ + exy
(c) y(4)^ − xy′′′^ = y′^ + exy
(d)
y − cos x y′′^ = ex
Problem 2 (12 Points))
For a given differential equation x^4 y′^ − xy^2 + 8x^5 = 0, solve the following questions.
(a) Find all values of C such that y = Cx^2 is a solution of this DE.
(b) Find the unique solution of the DE satisfying the initial condition y(3) = 36.
Problem 4 (16 Points)
Solve the IVP y′^ + 2x(y − 1) = 0, y(0) = 2.
Problem 5 (16 Points)
Solve the IVP
y′^ +
x y = x, y(1) = 1
Problem 6 (16 Points)
Solve the IVP 2 yy′^ = xex, y(0) = − 1