20094em3 Exercise 13

Engineering Mathematics 3

FIRST ORDER DIFFERETIAL EQUATIOS

Exactness Method Grade 50% off the total score within the first week after due date. Zero score after the first week. Name : Group: Subject: Topic: Date Due: Date of Submission:

Question 1.3.1

(

2

Question 1.3.8

)

(

Solve 2x⋅ y⋅ dx + 1 + x dy = 0

)

3

Solve 2t + 3y dt + ( 3t + y − 1) ⋅ dy = 0.

2

Ans: K = x ⋅ y + y

Ans: K =

1 4 1 2 ⋅ t + 3⋅ t⋅ y − y + ⋅ y 2 2

Question 1.3.2 Solve ( x + sin( y) ) ⋅ dx + ( x⋅ cos( y) − 2y) ⋅ dy = 0. 1 2 2 ⋅ x + sin( y) ⋅ x − y 2

Ans: K =

Question 1.3.3

(

2

)

Solve ( 2x⋅ y + x) ⋅ dx + x + y ⋅ dy = 0. 1 2 1 3 ⋅x + ⋅y 2 2

2

Ans: K = x ⋅ y +

Question 1.3.4

(

3

)

(

2 2

)

Solve y + 2⋅ x⋅ y dx + 1 + 3⋅ x ⋅ y + x ⋅ dy = 0 . 2 3

Ans: K = x⋅ y + x ⋅ y + y

Question 1.3.9

(

x⋅ y

Solve y⋅ e

x⋅ y

dx + x⋅ e

)

2

Solve t − y dt − t⋅ dy = 0 .

Question 1.3.5 dy = 0.

Ans: K = exp( x⋅ y)

Question 1.3.6

Ans: K =

1 3 ⋅ t − t⋅ y 3

Question 1.3.10

(

3t

)

3t

Solve y⋅ dx + x⋅ dy = 0.

Solve 3⋅ e ⋅ y − 2t dt + e dy = 0

Ans: K = x⋅ y

Ans: exp( 3⋅ t) ⋅ y − t

2

Question 1.3.7 Solve ( y⋅ sin( x) + x⋅ y⋅ cos( x) ) dx + ( x⋅ sin( x) + 1) dy = 0. Ans: K = − cos( x) ⋅ y + ( cos( x) + x⋅ sin( x) ) ⋅ y + y

20094em3 Exercise 13.mcd

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