20094em3 Exercise 11

Engineering Mathematics 3

FIRST ORDER DIFFERETIAL EQUATIOS

Separable 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 1.1.1 Solve Ans:

x⋅ y − x y

Question 1.1.6

dx + y⋅ dy = 0.

1 2 1 2 ⋅ x + y + ⋅ y + ln( y − 1) = K 2 2

2

y −8

Solve y' =

2

at y(x = 4) = 3.

y⋅ x + 16⋅ y

(

)

2

 x −π  4

Ans: 8⋅ ln⋅ y − 8 = 4⋅ atan 

Question 1.1.2 2

Question 1.1.7

3

Solve d

Solve x⋅ dx − y ⋅ dy = 0. 2

x 2 y 

Ans: 3x − 2y = K

2

= x ⋅ dx. at y(0) =1.

2 2

Ans: x ⋅ y = 3

Question 1.1.3 2 3

Solve y' = y ⋅ x .

Question 1.1.8

(

( 1 Ans: y − atan ( y) + ⋅ ln( x 2

−1

1 4 = ⋅x + K Ans: y 4

2

)

2

Ans: 2⋅ x − y = K

Ans: sec( x) + tan( y) = K

Question 1.1.5

Question 1.1.10

Solve

Ans:

dt

=

2

2

Solve sin( x) ⋅ cos( y) ⋅ dx + cos( x) ⋅ dy = 0

4

t−1

)

+1 =K

Question 1.1.9

3

Solve x⋅ dx − y ⋅ dy = 0.

dx

)

2

2

Question 1.1.4 2

2 2

Solve x y + y ⋅ dy + y ⋅ x + x ⋅ dx = 0.

.

y' =

Solve

x − 4x + 4

1 3 1 2 2 ⋅ x − 2⋅ x + 4⋅ x = − t + ⋅ t + K 3 2

20094em3 Exercise 11.mcd

2

x y+2

.

2

Ans: y + 4y = x + K

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