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)
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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