Differential equations

_____________________________________________________________________________________ Assignment 1, MATH 216, Sem. 382, JUC-Female Branch Page 1 of 6

JUBAIL UNIVERSITY COLLEGE

Semester 382 MATH 216 Assignment 1 Date of Submission: 5 -03-2018

Name: _______________________________ ID: ____________________ Section: 201

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

 

2 3

2

3

6 5 3 tan

cos

x ydy y x

dx x

  

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

(5 marks)

 2 2 , 0 8x y dx x dy y 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 4 2 2 36 2 9 8xy y x y x y y   (8 marks)

2.    2 22 cot csc 0xy y dx x x y dy   

IV. Find explicit (if convenient) general solution of the given differential equation. (6 marks)

_____________________________________________________________________________________ Assignment 1, MATH 216, Sem. 382, JUC-Female Branch Page 4 of 6

    22

9 1 0x dy y dx   

V. Solve the linear system of equations using Gaussian elimination. (6 marks)

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1 2 3 4

1 2 3 4

1 2 3 4

2 4 2 6

3 2 7 1

5 8 7 6 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. (3 marks)

1 4 5

2 4 5

3 4 5

4 0

3 5 0

7 0

x x x

x x x

x x x

  

  

  