Physics Exam > Physics Questions > The differential equation 2ydx – (3y &#...
Start Learning for Free
The differential equation 2ydx – (3y – 2x)dy = 0 is
- a)exact and homogeneous but not linear
- b)homogeneous and linear but not exact
- c)exact and linear but not homogeneous
- d)exact, homogeneous and linear
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The differential equation 2ydx – (3y – 2x)dy = 0 isa)exact...
2ydx + (2x – 3y)dy = 0 ...(1)
It is Homogeneous
M = 2y
Most Upvoted Answer
The differential equation 2ydx – (3y – 2x)dy = 0 isa)exact...
Given Differential Equation:
The given differential equation is 2ydx + (3y - 2x)dy = 0.
Explanation:
To analyze the given differential equation, we need to check for certain properties such as linearity, homogeneity, and exactness.
Linearity:
A differential equation is said to be linear if the dependent variable and its derivatives occur only in the first degree and are not multiplied together.
In the given equation, the term (3y - 2x)dy has the dependent variable y and its derivative dy occurring in the first degree, and they are not multiplied together. Hence, the given equation is linear.
Homogeneity:
A differential equation is said to be homogeneous if all the terms in the equation have the same degree with respect to the dependent variable and its derivatives.
In the given equation, the terms 2ydx and (3y - 2x)dy have the same degree with respect to y and its derivative dy. Hence, the given equation is homogeneous.
Exactness:
A differential equation is said to be exact if it can be expressed as the derivative of some function.
To check for exactness, we need to calculate the partial derivatives of the terms with respect to x and y.
The partial derivative of 2ydx with respect to y is 0, and the partial derivative of (3y - 2x)dy with respect to x is -2.
Since the partial derivatives are not equal, the given equation is not exact.
Conclusion:
Based on the above analysis, we can conclude that the given differential equation is homogeneous and linear but not exact (option B).
The given differential equation is 2ydx + (3y - 2x)dy = 0.
Explanation:
To analyze the given differential equation, we need to check for certain properties such as linearity, homogeneity, and exactness.
Linearity:
A differential equation is said to be linear if the dependent variable and its derivatives occur only in the first degree and are not multiplied together.
In the given equation, the term (3y - 2x)dy has the dependent variable y and its derivative dy occurring in the first degree, and they are not multiplied together. Hence, the given equation is linear.
Homogeneity:
A differential equation is said to be homogeneous if all the terms in the equation have the same degree with respect to the dependent variable and its derivatives.
In the given equation, the terms 2ydx and (3y - 2x)dy have the same degree with respect to y and its derivative dy. Hence, the given equation is homogeneous.
Exactness:
A differential equation is said to be exact if it can be expressed as the derivative of some function.
To check for exactness, we need to calculate the partial derivatives of the terms with respect to x and y.
The partial derivative of 2ydx with respect to y is 0, and the partial derivative of (3y - 2x)dy with respect to x is -2.
Since the partial derivatives are not equal, the given equation is not exact.
Conclusion:
Based on the above analysis, we can conclude that the given differential equation is homogeneous and linear but not exact (option B).
Free Test
FREE
| Start Free Test |
Community Answer
The differential equation 2ydx – (3y – 2x)dy = 0 isa)exact...
Exact and homogeneous but not linear
|
Explore Courses for Physics exam
|
|
Similar Physics Doubts
The differential equation 2ydx – (3y – 2x)dy = 0 isa)exact and homogeneous but not linearb)homogeneous and linear but not exactc)exact and linear but not homogeneousd)exact, homogeneous and linearCorrect answer is option 'A'. Can you explain this answer?
Question Description
The differential equation 2ydx – (3y – 2x)dy = 0 isa)exact and homogeneous but not linearb)homogeneous and linear but not exactc)exact and linear but not homogeneousd)exact, homogeneous and linearCorrect answer is option 'A'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about The differential equation 2ydx – (3y – 2x)dy = 0 isa)exact and homogeneous but not linearb)homogeneous and linear but not exactc)exact and linear but not homogeneousd)exact, homogeneous and linearCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The differential equation 2ydx – (3y – 2x)dy = 0 isa)exact and homogeneous but not linearb)homogeneous and linear but not exactc)exact and linear but not homogeneousd)exact, homogeneous and linearCorrect answer is option 'A'. Can you explain this answer?.
The differential equation 2ydx – (3y – 2x)dy = 0 isa)exact and homogeneous but not linearb)homogeneous and linear but not exactc)exact and linear but not homogeneousd)exact, homogeneous and linearCorrect answer is option 'A'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about The differential equation 2ydx – (3y – 2x)dy = 0 isa)exact and homogeneous but not linearb)homogeneous and linear but not exactc)exact and linear but not homogeneousd)exact, homogeneous and linearCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The differential equation 2ydx – (3y – 2x)dy = 0 isa)exact and homogeneous but not linearb)homogeneous and linear but not exactc)exact and linear but not homogeneousd)exact, homogeneous and linearCorrect answer is option 'A'. Can you explain this answer?.
Solutions for The differential equation 2ydx – (3y – 2x)dy = 0 isa)exact and homogeneous but not linearb)homogeneous and linear but not exactc)exact and linear but not homogeneousd)exact, homogeneous and linearCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Physics.
Download more important topics, notes, lectures and mock test series for Physics Exam by signing up for free.
Here you can find the meaning of The differential equation 2ydx – (3y – 2x)dy = 0 isa)exact and homogeneous but not linearb)homogeneous and linear but not exactc)exact and linear but not homogeneousd)exact, homogeneous and linearCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The differential equation 2ydx – (3y – 2x)dy = 0 isa)exact and homogeneous but not linearb)homogeneous and linear but not exactc)exact and linear but not homogeneousd)exact, homogeneous and linearCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for The differential equation 2ydx – (3y – 2x)dy = 0 isa)exact and homogeneous but not linearb)homogeneous and linear but not exactc)exact and linear but not homogeneousd)exact, homogeneous and linearCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of The differential equation 2ydx – (3y – 2x)dy = 0 isa)exact and homogeneous but not linearb)homogeneous and linear but not exactc)exact and linear but not homogeneousd)exact, homogeneous and linearCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The differential equation 2ydx – (3y – 2x)dy = 0 isa)exact and homogeneous but not linearb)homogeneous and linear but not exactc)exact and linear but not homogeneousd)exact, homogeneous and linearCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Physics tests.
|
|
Explore Courses for Physics exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup