Jaypee Institute of Information Technology (JIIT) 2008 B.E Test 1 : Mathematics II For All - Question Paper

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JAYPEE UNIVERSITY OF INFORMATION TECHNOLOGY

WAKNAGHAT (H. P.)

TEST - 1 (February 200S)

B. Tcch. (BI, BT, BTDD. CE) Semester II

CourseCode: 07B21MA102 Max. Time: 1 Hour

Course Title: Mathematics 11

Course Credits: 4 Max. Marks: 20

i\ote: Attempt all questions. Marks for each question are given on right in brackets.

y

1. Solve the differential equation x y - xy + y = 2 log x by taking log* * z . (5)

1 1

2. Obtain the general solution of the equation x y" - 2xy' + (x + 2)y - 0. (5)

3. Test whether the series

, 1 1 1 1 1 I I

2 2 *^,+ 2⁺ 2~ 2~2 ⁺....................

2 3J 4- 5 I2 8

is convergent or not? (2)

Find the interval of convcrgcncc of the series

2 2³*³ , 4 2¹x⁵ 2x--+ 4.x--+.....................

Obtain two independent power series solutions near x 0 of the differential

equation y" + xy = 0. (5)

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