Class CBSE Class 12 Mathematics Differential Equations Q #813
KNOWLEDGE BASED
APPLY
1 Marks 2023 MCQ SINGLE
11. The order and degree (if defined) of the differential equation, $(\frac{d^{2}y}{dx^{2}})^{2}+(\frac{dy}{dx})^{2}=x\sin(\frac{dy}{dx})$ respectively are :
(A) 2, 2
(B) 1, 3
(C) 2, 3
(D) 2, degree not defined
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Step-by-Step Solution

  1. Identify the order: The order of a differential equation is the highest order derivative present in the equation. In this case, the highest order derivative is $\frac{d^{2}y}{dx^{2}}$, which is the second derivative. Therefore, the order is 2.

  2. Identify the degree: The degree of a differential equation is the power of the highest order derivative, provided the equation is a polynomial equation in derivatives. However, in the given equation, we have the term $\sin(\frac{dy}{dx})$. Since the derivative is inside a trigonometric function, the equation is not a polynomial equation in derivatives, and therefore, the degree is not defined.

  3. Conclusion: The order is 2, and the degree is not defined.

Correct Answer: 2, degree not defined

AI Suggestion: Option D

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply their understanding of order and degree of differential equations to identify them in the given equation.
Knowledge Dimension: CONCEPTUAL
Justification: The question requires understanding the concepts of order and degree of a differential equation, rather than just recalling facts or following a specific procedure. The presence of $\sin(\frac{dy}{dx})$ makes the degree undefined.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the knowledge of order and degree of differential equations as defined in the textbook.

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