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_____________________________________________________________________________________ Assignment 1, MATH 216, Sem. 372, JUC-Female Branch Page 1 of 6

JUBAIL UNIVERSITY COLLEGE Semester 372 MATH 216 Assignment 1 Date of Submission: 21 -03-2017

Name: _________________________________ ID: ____________________ Section: 201

I. Solve the Bernoulli’s differential equation. (7 marks)

2 2

3 2

4

dy x y

dx xy

  

_____________________________________________________________________________________ Assignment 1, MATH 216, Sem. 372, JUC-Female Branch Page 2 of 6

II. Find the particular solution of the homogeneous differential equation with the given initial condition.

(5 marks)

   3 , 1 0x dy y xy dx y  

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III. Determine whether the given differential equations are exact. If it is exact, then find its general solution.

1.    3 28 3 3 1x y x dy y x dx    (10 marks)

2.    2 22 tan sec 0xy y dx x x y dy   

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IV. Find explicit (if convenient) general solution of the given differential equation. (5 marks)

    22

4 1 0x dy y dx   

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V. Solve the linear system of equations using Gaussian elimination. (8 marks)

1 2 3 4

1 2 3 4

1 2 3 4

2 3 3 11

2 2 8 1

4

x x x x

x x x x

x x x x

   

    

    

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VI. Find the solution in a vector form of the given system. (5 marks)

1 4 5

2 4 5

3 4 5

3 0

2 6 0

8 0

x x x

x x x

x x x

  

  

  