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The value of 
where ‘C’ is the curve passing through the point (0, √2) and satisfying the differential equation dy/dx = −2x/y is ________.
where ‘C’ is the curve passing through the point (0, √2) and satisfying the differential equation dy/dx = −2x/y is ________.Correct answer is between '-5,-4'. Can you explain this answer?
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Most Upvoted Answer
The value of where ‘C’ is the curve passing through the p...
Concept:
Green's theorem converts the line integral to a double integral.
Green's theorem transform the line integral in xy - plane to a surface integral on the same xy - plane
If P and Q are functions of (x, y) defined in an open region then
Application:
Given the differential equation is:
y dy = -2 xdx
C = 1
∴ The equation of a curve is:
This is an ellipse.
On comparing with 
we get:
we get:a = 1 and b = √2
Now, the given integral is:
(4y – 3x)dx + (3x + 2y) dy
Here M = 4y – 3x and N = 3x + 2y
Applying Greens theorem, we convert the line integral to a double integral, i.e.
∴ The given integral becomes:
= 
= - (Area under ellipse)
= 
= 
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Community Answer
The value of where ‘C’ is the curve passing through the p...
Concept:
Green's theorem converts the line integral to a double integral.
Green's theorem transform the line integral in xy - plane to a surface integral on the same xy - plane
If P and Q are functions of (x, y) defined in an open region then
Application:
Given the differential equation is:
y dy = -2 xdx
C = 1
∴ The equation of a curve is:
This is an ellipse.
On comparing with we get:
we get:a = 1 and b = √2
Now, the given integral is:
(4y – 3x)dx + (3x + 2y) dy
Here M = 4y – 3x and N = 3x + 2y
Applying Greens theorem, we convert the line integral to a double integral, i.e.
∴ The given integral becomes:
=
= - (Area under ellipse)
=
=
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The value of where ‘C’ is the curve passing through the point (0, √2) and satisfying the differential equationdy/dx = −2x/y is ________.Correct answer is between '-5,-4'. Can you explain this answer?
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The value of where ‘C’ is the curve passing through the point (0, √2) and satisfying the differential equationdy/dx = −2x/y is ________.Correct answer is between '-5,-4'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The value of where ‘C’ is the curve passing through the point (0, √2) and satisfying the differential equationdy/dx = −2x/y is ________.Correct answer is between '-5,-4'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The value of where ‘C’ is the curve passing through the point (0, √2) and satisfying the differential equationdy/dx = −2x/y is ________.Correct answer is between '-5,-4'. Can you explain this answer?.
The value of where ‘C’ is the curve passing through the point (0, √2) and satisfying the differential equationdy/dx = −2x/y is ________.Correct answer is between '-5,-4'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The value of where ‘C’ is the curve passing through the point (0, √2) and satisfying the differential equationdy/dx = −2x/y is ________.Correct answer is between '-5,-4'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The value of where ‘C’ is the curve passing through the point (0, √2) and satisfying the differential equationdy/dx = −2x/y is ________.Correct answer is between '-5,-4'. Can you explain this answer?.
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