(a) To show: If ∂ N / ∂ x − ∂ M / ∂ y / x M − y N depends only on the product x y then the equation M ( x , y ) d x + N ( x , y ) d y = 0 has an integrating factor of the form μ ( x y ) and also give the general formula for μ ( x y ) .

Question

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Answer 1

Question

Chapter 2.5, Problem 15E

To determine

(a)

To show:

If ∂N/∂x−∂M/∂y/xM−yN depends only on the product xy then the equation M(x,y)dx+ N(x,y)dy=0 has an integrating factor of the form μ(xy) and also give the general formula for μ(xy).

To determine

(b)

The implicit solution for the differential equation (3y+2xy2)dx+(x + 2x2y)dy=0 satisfying the initial condition y(1)=1.

Expert Solution & Answer

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Answer 2

Question

Chapter 2.5, Problem 15E

To determine

(a)

To show:

If ∂N/∂x−∂M/∂y/xM−yN depends only on the product xy then the equation M(x,y)dx+ N(x,y)dy=0 has an integrating factor of the form μ(xy) and also give the general formula for μ(xy).

To determine

(b)

The implicit solution for the differential equation (3y+2xy2)dx+(x + 2x2y)dy=0 satisfying the initial condition y(1)=1.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 2.5, Problem 15E

To determine

(a)

To show:

If ∂N/∂x−∂M/∂y/xM−yN depends only on the product xy then the equation M(x,y)dx+ N(x,y)dy=0 has an integrating factor of the form μ(xy) and also give the general formula for μ(xy).

To determine

(b)

The implicit solution for the differential equation (3y+2xy2)dx+(x + 2x2y)dy=0 satisfying the initial condition y(1)=1.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 2.5, Problem 15E

To determine

(a)

To show:

If ∂N/∂x−∂M/∂y/xM−yN depends only on the product xy then the equation M(x,y)dx+ N(x,y)dy=0 has an integrating factor of the form μ(xy) and also give the general formula for μ(xy).

To determine

(b)

The implicit solution for the differential equation (3y+2xy2)dx+(x + 2x2y)dy=0 satisfying the initial condition y(1)=1.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 2.5, Problem 15E

To determine

(a)

To show:

If ∂N/∂x−∂M/∂y/xM−yN depends only on the product xy then the equation M(x,y)dx+ N(x,y)dy=0 has an integrating factor of the form μ(xy) and also give the general formula for μ(xy).

To determine

(b)

The implicit solution for the differential equation (3y+2xy2)dx+(x + 2x2y)dy=0 satisfying the initial condition y(1)=1.

Answer 6

Chapter 2.5, Problem 15E

To determine

(a)

To show:

If ∂N/∂x−∂M/∂y/xM−yN depends only on the product xy then the equation M(x,y)dx+ N(x,y)dy=0 has an integrating factor of the form μ(xy) and also give the general formula for μ(xy).

Answer 7

Chapter 2.5, Problem 15E

To determine

(a)

To show:

If ∂N/∂x−∂M/∂y/xM−yN depends only on the product xy then the equation M(x,y)dx+ N(x,y)dy=0 has an integrating factor of the form μ(xy) and also give the general formula for μ(xy).

Answer 8

To determine

(b)

The implicit solution for the differential equation (3y+2xy2)dx+(x + 2x2y)dy=0 satisfying the initial condition y(1)=1.

Answer 9

To determine

(b)

The implicit solution for the differential equation (3y+2xy2)dx+(x + 2x2y)dy=0 satisfying the initial condition y(1)=1.

Answer 10

Expert Solution & Answer

Answer 11

Expert Solution & Answer

Answer 12

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Answer 13

Ch. 2.2 - Prob. 1E Ch. 2.2 - In Problems 1-6, determine whether the given...Ch. 2.2 - Prob. 3E Ch. 2.2 - Prob. 4E Ch. 2.2 - Prob. 5E Ch. 2.2 - Prob. 6E Ch. 2.2 - Prob. 7E Ch. 2.2 - Prob. 8E Ch. 2.2 - Prob. 9E Ch. 2.2 - Prob. 10E

(a) To show: If ∂ N / ∂ x − ∂ M / ∂ y / x M − y N depends only on the product x y then the equation M ( x , y ) d x + N ( x , y ) d y = 0 has an integrating factor of the form μ ( x y ) and also give the general formula for μ ( x y ) .

(a) To show: If ∂N/∂x−∂M/∂y/xM−yN depends only on the product xy then the equation M(x,y)dx+ N(x,y)dy=0 has an integrating factor of the form μ(xy) and also give the general formula for μ(xy).

(b) The implicit solution for the differential equation (3y+2xy2)dx+(x + 2x2y)dy=0 satisfying the initial condition y(1)=1.

Want to see the full answer?

Chapter 2 Solutions

(a)

To show:

If ∂N/∂x−∂M/∂y/xM−yN depends only on the product xy then the equation M(x,y)dx+ N(x,y)dy=0 has an integrating factor of the form μ(xy) and also give the general formula for μ(xy).

(b)

The implicit solution for the differential equation (3y+2xy2)dx+(x + 2x2y)dy=0 satisfying the initial condition y(1)=1.