Marist Brothers First Trinal Examinations Notre Dame of Kidapawan College July 14-16, 2015 First Semester, SY 2015-2016 MATH311 Differential Equations Kidapawan City Mar Lou P. Galinato, ECE, MEP Name: ___________________________________________ Program/Year: _______________________
INSTRUCTION: Shade only the letter of your choice to each item. Erasures will be considered wrong. Show your solution (detailed) for items 7 to 12 on provided newsprints. [1] [2 PTS] The following are examples of
differential equations except
[A] (2
2)
3
+ = 0
[B]
+
=
[C] 2
2+
+
1
= cos
[D] 3 + = (, )
[2] [2 PTS] When an equation involves one or more derivatives with respect to a particular variable, that variable is called [A] dependent variable [B] independent variable [C] parameters [D] arbitrary constant
[3] [2 PTS] What is the independent variable of
the equation 2
2+
+
1
= cos ?
[A] [B] , , , , [C] [D]
[4] [2 PTS] Which of the following differential
equations that has one dependent variable and two independent variable?
[A]
= 2 (
2
2+
2
2)
[B] (2 + 2) 2 = 0
[C] 2
2+
2
2= 0
[D] 2
2+ 2 (
)
3+ = 0
[5] [2 PTS] What is the order of the differential
equation 2
2+ 2 (
)
3+ = 0?
[A] order one [B] order two [C] first-order [D] third-order
[6] [2 PTS] The following differential equations are considered linear except [A] 2 + + (2 2) = 43
[B] 0(, )
+ 1(, )
= (, )
[C] 3 + 2 = 0
[D] 2
2+
6 = 0
[7] [10 PTS] What is the differential equation
after eliminating and from the relation = cos( + )?
[A] 2
2+ 22 = 0
[B] 2
2+ = 0
[C] 2
2+ 2 = 0
[D] 2
2+ 2 = 0
[8] [10 PTS] Eliminating the arbitrary constants
1 2 considering as parameters in the relation = 1
cos + 2 sin ,
will result to a differential equation which is [A] 2 + (2 + 2) = 0 [B] 3 + (2 + 2) = 0 [C] 4 + (2 + 2) = 0 [D] 4 5 + (2 + 2) = 0
[9] [10 PTS] The differential equation +
()2 + 1 = 0 is a family of [A] Circles with center at the origin [B] Circles with center on the x-axis [C] Circles tangent to the x-axis [D] Straight lines with slope and x-intercept
equal
[10] [10 PTS] The differential equation 2 = 1 is a family of [A] Parabolas with axis parallel to the y-axis
and with distance from vertex to focus fixed as .
[B] Parabolas with axis parallel to the x-axis and with distance from vertex to focus fixed as .
[C] Parabolas with vertex and focus on the x-axis.
[D] Parabolas with axis parallel to the x-axis.
[11] [50 PTS] Which of the following relations is the general solution of the differential equation 3 2(3) + 3() 2() = 0? [A] 1
2
1
12sin(6) =
3
22 +
1
5[cos()]5
1
3[cos()]3 +
[B] 12
+1
9sin(3) =
3
22 +
1
5[cos(2)]5
1
5[cos()]3 +
[C] 12
1
6sin(2) =
3
22 +
1
5[cos(4)]5
1
2[cos()]3 +
[D] 12
+1
4sin(4) =
3
22 +
1
5[cos(5)]5
1
4[cos()]3 +
[12] [50 PTS] Which of the following relations is
the general solution of the differential equation 43 1 2(53 32) = 1 2(2 1) 23?
[A] 13
(1 + 2)3
1 2 = 4 ln|| 1
+
3
2ln|2 + 5|
2 tan1() +
[B] 13
(1 2)3
+ 1 2 = 2 ln|| 1
+
3
7ln|2 + 1|
2 tan1() +
[C] 13
(1 2)3
1 2 = 2 ln|| +1
+
9
2ln|2 + 1|
2 tan1() +
[D] 13
(1 2)3
1 2 = 2 ln|| 1
+
3
2ln|2 + 1|
2 tan1() +
-x-x-x-x-x-x-x-x- NOTHING FOLLOWS -x-x-x-x-x-x-x-x-