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-