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Solve the following equation:
yexydx + (xexy + 2y)dy = 0
yexydx + (xexy + 2y)dy = 0
- a)xexy + 2y2 = c
- b)xexy + y2 = c
- c)exy + 2y2 = c
- d)exy + y2 = c
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Solve the following equation:yexydx + (xexy + 2y)dy = 0a)xexy + 2y2 = ...
The given equation is in the form of
M dx + N dy = 0
Here M = y exy
N = (x exy + 2y)
Hence the differential equation is an exact equation.
The solution is
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Solve the following equation:yexydx + (xexy + 2y)dy = 0a)xexy + 2y2 = ...
To solve the given equation, we need to separate the variables and integrate both sides with respect to their respective variables.
Given equation:
∫yexydx + ∫(xexy - 2y)dy = 0
Now let's solve each integral separately.
1. Integral with respect to x:
We can use integration by parts for the first integral. Let u = y and dv = exydx. Then du = dy and v = ∫exydx.
Using the integration by parts formula:
∫yexydx = y∫exydx - ∫(dy/ dx)∫exydx
= y∫exydx - ∫(1)(∫exydx)
= yexy - ∫exydx
2. Integral with respect to y:
∫(xexy - 2y)dy = ∫(xexy)dy - ∫(2y)dy
= x∫exydy - 2∫ydy
= xexy - y^2
Now let's substitute the results of the integrals back into the original equation:
yexy - ∫exydx + xexy - y^2 = 0
Combining like terms:
2yexy - y^2 - ∫exydx = 0
Rearranging the equation:
∫exydx = 2yexy - y^2
Comparing this equation with the given options:
exy - y^2 = c
We can see that the correct answer is option D: exy - y^2 = c.
Given equation:
∫yexydx + ∫(xexy - 2y)dy = 0
Now let's solve each integral separately.
1. Integral with respect to x:
We can use integration by parts for the first integral. Let u = y and dv = exydx. Then du = dy and v = ∫exydx.
Using the integration by parts formula:
∫yexydx = y∫exydx - ∫(dy/ dx)∫exydx
= y∫exydx - ∫(1)(∫exydx)
= yexy - ∫exydx
2. Integral with respect to y:
∫(xexy - 2y)dy = ∫(xexy)dy - ∫(2y)dy
= x∫exydy - 2∫ydy
= xexy - y^2
Now let's substitute the results of the integrals back into the original equation:
yexy - ∫exydx + xexy - y^2 = 0
Combining like terms:
2yexy - y^2 - ∫exydx = 0
Rearranging the equation:
∫exydx = 2yexy - y^2
Comparing this equation with the given options:
exy - y^2 = c
We can see that the correct answer is option D: exy - y^2 = c.
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Solve the following equation:yexydx + (xexy + 2y)dy = 0a)xexy + 2y2 = cb)xexy + y2 = cc)exy + 2y2 = cd)exy + y2 = cCorrect answer is option 'D'. Can you explain this answer?
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Solve the following equation:yexydx + (xexy + 2y)dy = 0a)xexy + 2y2 = cb)xexy + y2 = cc)exy + 2y2 = cd)exy + y2 = cCorrect answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Solve the following equation:yexydx + (xexy + 2y)dy = 0a)xexy + 2y2 = cb)xexy + y2 = cc)exy + 2y2 = cd)exy + y2 = cCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve the following equation:yexydx + (xexy + 2y)dy = 0a)xexy + 2y2 = cb)xexy + y2 = cc)exy + 2y2 = cd)exy + y2 = cCorrect answer is option 'D'. Can you explain this answer?.
Solve the following equation:yexydx + (xexy + 2y)dy = 0a)xexy + 2y2 = cb)xexy + y2 = cc)exy + 2y2 = cd)exy + y2 = cCorrect answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Solve the following equation:yexydx + (xexy + 2y)dy = 0a)xexy + 2y2 = cb)xexy + y2 = cc)exy + 2y2 = cd)exy + y2 = cCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve the following equation:yexydx + (xexy + 2y)dy = 0a)xexy + 2y2 = cb)xexy + y2 = cc)exy + 2y2 = cd)exy + y2 = cCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Solve the following equation:yexydx + (xexy + 2y)dy = 0a)xexy + 2y2 = cb)xexy + y2 = cc)exy + 2y2 = cd)exy + y2 = cCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
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Solve the following equation:yexydx + (xexy + 2y)dy = 0a)xexy + 2y2 = cb)xexy + y2 = cc)exy + 2y2 = cd)exy + y2 = cCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Solve the following equation:yexydx + (xexy + 2y)dy = 0a)xexy + 2y2 = cb)xexy + y2 = cc)exy + 2y2 = cd)exy + y2 = cCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Solve the following equation:yexydx + (xexy + 2y)dy = 0a)xexy + 2y2 = cb)xexy + y2 = cc)exy + 2y2 = cd)exy + y2 = cCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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