Class CBSE Class 12 Mathematics Differential Equations Q #815
KNOWLEDGE BASED
APPLY
1 Marks 2023 MCQ SINGLE
What is the product of the order and degree of the differential equation $\frac{d^{2}y}{dx^{2}}\sin y+(\frac{dy}{dx})^{3}\cos y=\sqrt{y}$ ?
(A) 3
(B) 2
(C) 6
(D) not defined
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AI Tutor Explanation

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Step-by-Step Solution

  1. Step 1: Identify the order of the differential equation.

    The order of a differential equation is the highest order derivative present in the equation. In the given equation, $\frac{d^{2}y}{dx^{2}}$ is the highest order derivative, which is of order 2.

  2. Step 2: Identify the degree of the differential equation.

    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, $\frac{d^{2}y}{dx^{2}}$ is inside the $\sin$ function, which means the equation is not a polynomial equation in derivatives. Therefore, the degree is not defined.

  3. Step 3: Determine the product of the order and degree.

    Since the degree is not defined, the product of the order and degree is also not defined.

Correct Answer: 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 determine the correct answer.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a procedure to identify the order and degree of the given differential equation and then compute their product.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's knowledge of the definitions of order and degree of a differential equation as covered in the textbook.

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