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General solution of y log y dx – x dy = 0
- a)y = e−cx
- b)y = ecx+ e−cx
- c)y = ecx
- d)y2 = ecx
Correct answer is option 'C'. Can you explain this answer?
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General solution of y log y dx – x dy = 0a)y=e−cxb)y=ecx+e...
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General solution of y log y dx – x dy = 0a)y=e−cxb)y=ecx+e...
Understanding the Differential Equation
The given equation is:
y log y dx + x dy = 0
This can be rearranged to isolate dy:
y log y dx = -x dy
This indicates a relationship between y and x, allowing us to investigate further.
Separation of Variables
To solve, express the equation in a separable form:
dy/y log y = -dx/x
Now, we can integrate both sides.
Integrating Both Sides
Perform the integration:
- The left side involves the integral of dy/y log y, which requires a substitution or special function.
- The right side integrates to give -log|x| + C, where C is the constant of integration.
After performing the integration, we can express the results in a manageable form.
General Solution
The general solution derived from the integration leads to:
y^2 = e^(cx)
This fits option 'C', confirming that y can be expressed as a function of x.
Conclusion
Thus, the solution y^2 = e^(cx) encapsulates the relationship defined by the original differential equation, making option 'C' the correct answer. Understanding this solution involves recognizing how to manipulate and integrate the terms within the given equation.
The given equation is:
y log y dx + x dy = 0
This can be rearranged to isolate dy:
y log y dx = -x dy
This indicates a relationship between y and x, allowing us to investigate further.
Separation of Variables
To solve, express the equation in a separable form:
dy/y log y = -dx/x
Now, we can integrate both sides.
Integrating Both Sides
Perform the integration:
- The left side involves the integral of dy/y log y, which requires a substitution or special function.
- The right side integrates to give -log|x| + C, where C is the constant of integration.
After performing the integration, we can express the results in a manageable form.
General Solution
The general solution derived from the integration leads to:
y^2 = e^(cx)
This fits option 'C', confirming that y can be expressed as a function of x.
Conclusion
Thus, the solution y^2 = e^(cx) encapsulates the relationship defined by the original differential equation, making option 'C' the correct answer. Understanding this solution involves recognizing how to manipulate and integrate the terms within the given equation.
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General solution of y log y dx – x dy = 0a)y=e−cxb)y=ecx+e−cxc)y=ecxd)y2 =ecxCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about General solution of y log y dx – x dy = 0a)y=e−cxb)y=ecx+e−cxc)y=ecxd)y2 =ecxCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for General solution of y log y dx – x dy = 0a)y=e−cxb)y=ecx+e−cxc)y=ecxd)y2 =ecxCorrect answer is option 'C'. Can you explain this answer?.
General solution of y log y dx – x dy = 0a)y=e−cxb)y=ecx+e−cxc)y=ecxd)y2 =ecxCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about General solution of y log y dx – x dy = 0a)y=e−cxb)y=ecx+e−cxc)y=ecxd)y2 =ecxCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for General solution of y log y dx – x dy = 0a)y=e−cxb)y=ecx+e−cxc)y=ecxd)y2 =ecxCorrect answer is option 'C'. Can you explain this answer?.
Solutions for General solution of y log y dx – x dy = 0a)y=e−cxb)y=ecx+e−cxc)y=ecxd)y2 =ecxCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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