20094em3 Exercise 12

Engineering Mathematics 3

FIRST ORDER DIFFERETIAL EQUATIOS

Reducible Homogeneous 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 1.2.1 Solve

dx

Question 1.2.5

x+y

dy =

x y

Ans: ln( K⋅ x) =

Solve

dx

x

4

x⋅ y

 y4 ⋅ ln 4  x4  1

−y x

2y + x

dy Solve

3

Ans: ln( K⋅ x) =

x

Question 1.2.6

4

2⋅ y + x =

dx

=

Ans: ln( k⋅ x) =

Question 1.2.2 dy

y−x

dy Solve

dx

=

x

 

 + 1  

Ans: ln( K⋅ x) = ln1 +

y



x

Question 1.2.7 Question 1.2.3 2

dx

Solve

x +y

dy Solve

=

2

dx

=

2⋅ x⋅ y

x⋅ y Ans: ln( K⋅ x) =

2

Ans: ln( K⋅ x) =

1 y ⋅ 2 2 x

2

x −y

dy

2

−1 3

.

   

⋅ ln 3⋅

2

y

2

x

   

−1

Question 1.2.4 2⋅ x⋅ y

dy Solve

dx

=

Ans: ln( k⋅ x)

2

2

x −y

  y  = ln  − ln 1 +   x 

20094em3 Exercise 12.mcd

2

y



2

x



Copyright 2008 - 2009

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Engineering Mathematics 3

Question 1.2.8 2

dx

2

x +y

dy Solve

=

.

2⋅ x⋅ y

 

Ans: ln( K⋅ x) = − ln−1 +

y

 y  − ln1 +  x  x

Question 1.2.9 2

xy + y

dy Solve

dx

.

=

2

x

2

x y Ans:

=K

2x + y

Question 1.2.10 Solve y' =

3x⋅ y 2

2

.

y +x Ans: ln( K⋅ x) =

1 2

 y −  x

⋅ ln

20094em3 Exercise 12.mcd

3 4

   

⋅ ln − 2 +

2

y



2

x



Copyright 2008 - 2009

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