Class CBSE Class 12 Mathematics Differential Equations Q #810
KNOWLEDGE BASED
UNDERSTAND
1 Marks 2023 MCQ SINGLE
The sum of the order and the degree of the differential equation \frac{d^{2}y}{dx^{2}}+(\frac{dy}{dx})^{3}=sin\~y is:
(A) 5
(B) 2
(C) 3
(D) 4
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AI Tutor Explanation

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Step-by-Step Solution

  1. The order of a differential equation is the highest order derivative present in the equation. In this case, it is 2 (from \(\frac{d^{2}y}{dx^{2}}\)).
  2. The degree of a differential equation is the power of the highest order derivative, provided the equation is a polynomial equation in its derivatives. Here, the highest order derivative is \(\frac{d^{2}y}{dx^{2}}\), and its power is 1.
  3. The sum of the order and degree is 2 + 1 = 3.

Correct Answer: 3

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 definitions of order and degree of a differential equation to answer it.
Knowledge Dimension: CONCEPTUAL
Justification: The question requires understanding the concepts of order and degree of a differential equation, rather than just recalling facts or applying a specific procedure.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the understanding of definitions related to differential equations as covered in the textbook.

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