Class CBSE Class 12 Mathematics Differential Equations Q #814
KNOWLEDGE BASED
UNDERSTAND
1 Marks 2023 MCQ SINGLE
The solution of the differential equation $\frac{dx}{x}+\frac{dy}{y}=0$ is:
(A) $\frac{1}{x}+\frac{1}{y}=C$
(B) $\log x-\log y=C$
(C) $xy=C$
(D) $x+y=C$
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Step-by-Step Solution

Given the differential equation: $\frac{dx}{x} + \frac{dy}{y} = 0$

Integrate both sides:

$\int \frac{dx}{x} + \int \frac{dy}{y} = \int 0$

$\log |x| + \log |y| = C'$ where $C'$ is the constant of integration.

Using the logarithm property $\log a + \log b = \log (ab)$:

$\log |xy| = C'$

Taking the exponential of both sides:

$|xy| = e^{C'}$

Since $e^{C'}$ is a constant, we can replace it with another constant $C$:

$xy = C$

Correct Answer: xy=C

AI Suggestion: Option C

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Pedagogical Audit
Bloom's Analysis: This is an UNDERSTAND question because the student needs to understand the process of solving a simple differential equation by separation of variables.
Knowledge Dimension: CONCEPTUAL
Justification: The question requires understanding the concept of differential equations and how to solve them using separation of variables.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the knowledge of solving differential equations, a standard topic in the syllabus.

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