(a) To prove: The one-parameter family solution of the equation ( 4 x y + 3 x 2 ) d x + ( 2 y + 2 x 2 ) d y = 0 is x 3 + 2 x 2 y + y 2 = c .

Question

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Answer 1

Question

Chapter 2.4, Problem 39E

To determine

(a)

To prove: The one-parameter family solution of the equation (4xy+3x2)dx+(2y+2x2)dy=0 is x3+2x2y+y2=c.

To determine

(b)

To prove: The initial conditions y(0)=−2 and y(1)=1 determine the same implicit solution.

To determine

(c)

The explicit solutions y1(x) and y2(x) of differential equation such that y1(0)=−2 and y2(1)=1.

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(a) Form the difference equation whose solution is yk = ci + (c2 + c3k)(-1)*, where c1, c2 and cs are arbitrary constant.

Answer 2

Question

Chapter 2.4, Problem 39E

To determine

(a)

To prove: The one-parameter family solution of the equation (4xy+3x2)dx+(2y+2x2)dy=0 is x3+2x2y+y2=c.

To determine

(b)

To prove: The initial conditions y(0)=−2 and y(1)=1 determine the same implicit solution.

To determine

(c)

The explicit solutions y1(x) and y2(x) of differential equation such that y1(0)=−2 and y2(1)=1.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 2.4, Problem 39E

To determine

(a)

To prove: The one-parameter family solution of the equation (4xy+3x2)dx+(2y+2x2)dy=0 is x3+2x2y+y2=c.

To determine

(b)

To prove: The initial conditions y(0)=−2 and y(1)=1 determine the same implicit solution.

To determine

(c)

The explicit solutions y1(x) and y2(x) of differential equation such that y1(0)=−2 and y2(1)=1.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 2.4, Problem 39E

To determine

(a)

To prove: The one-parameter family solution of the equation (4xy+3x2)dx+(2y+2x2)dy=0 is x3+2x2y+y2=c.

To determine

(b)

To prove: The initial conditions y(0)=−2 and y(1)=1 determine the same implicit solution.

To determine

(c)

The explicit solutions y1(x) and y2(x) of differential equation such that y1(0)=−2 and y2(1)=1.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 2.4, Problem 39E

To determine

(a)

To prove: The one-parameter family solution of the equation (4xy+3x2)dx+(2y+2x2)dy=0 is x3+2x2y+y2=c.

To determine

(b)

To prove: The initial conditions y(0)=−2 and y(1)=1 determine the same implicit solution.

To determine

(c)

The explicit solutions y1(x) and y2(x) of differential equation such that y1(0)=−2 and y2(1)=1.

Answer 6

Chapter 2.4, Problem 39E

To determine

(a)

To prove: The one-parameter family solution of the equation (4xy+3x2)dx+(2y+2x2)dy=0 is x3+2x2y+y2=c.

Answer 7

Chapter 2.4, Problem 39E

To determine

(a)

To prove: The one-parameter family solution of the equation (4xy+3x2)dx+(2y+2x2)dy=0 is x3+2x2y+y2=c.

Answer 8

To determine

(b)

To prove: The initial conditions y(0)=−2 and y(1)=1 determine the same implicit solution.

Answer 9

To determine

(b)

To prove: The initial conditions y(0)=−2 and y(1)=1 determine the same implicit solution.

Answer 10

To determine

(c)

The explicit solutions y1(x) and y2(x) of differential equation such that y1(0)=−2 and y2(1)=1.

Answer 11

To determine

(c)

The explicit solutions y1(x) and y2(x) of differential equation such that y1(0)=−2 and y2(1)=1.

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E

(a) To prove: The one-parameter family solution of the equation ( 4 x y + 3 x 2 ) d x + ( 2 y + 2 x 2 ) d y = 0 is x 3 + 2 x 2 y + y 2 = c .

Concept explainers

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(a)

To prove: The one-parameter family solution of the equation (4xy+3x2)dx+(2y+2x2)dy=0 is x3+2x2y+y2=c.

(b)

To prove: The initial conditions y(0)=−2 and y(1)=1 determine the same implicit solution.

(c)

The explicit solutions y1(x) and y2(x) of differential equation such that y1(0)=−2 and y2(1)=1.

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Chapter 2 Solutions

(a) To prove: The one-parameter family solution of the equation ( 4 x y + 3 x 2 ) d x + ( 2 y + 2 x 2 ) d y = 0 is x 3 + 2 x 2 y + y 2 = c .

Concept explainers

Videos

(a) To prove: The one-parameter family solution of the equation (4xy+3x2)dx+(2y+2x2)dy=0 is x3+2x2y+y2=c.

(b) To prove: The initial conditions y(0)=−2 and y(1)=1 determine the same implicit solution.

(c) The explicit solutions y1(x) and y2(x) of differential equation such that y1(0)=−2 and y2(1)=1.

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Chapter 2 Solutions

(a)

To prove: The one-parameter family solution of the equation (4xy+3x2)dx+(2y+2x2)dy=0 is x3+2x2y+y2=c.

(b)

To prove: The initial conditions y(0)=−2 and y(1)=1 determine the same implicit solution.

(c)

The explicit solutions y1(x) and y2(x) of differential equation such that y1(0)=−2 and y2(1)=1.