Class CBSE Class 12 Mathematics Differential Equations Q #649
KNOWLEDGE BASED
APPLY
1 Marks 2024 AISSCE(Board Exam) MCQ SINGLE
The order and degree of the differential equation \([1+(\frac{dy}{dx})^{2}]^{3}=\frac{d^{2}y}{dx^{2}}\) respectively are:
(A) 1, 2
(B) 2, 3
(C) 2, 1
(D) 2, 6
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Correct Answer: C

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Step-by-Step Solution

  1. First, rewrite the given differential equation to eliminate the radical: \([1+(\frac{dy}{dx})^{2}]^{3}=\frac{d^{2}y}{dx^{2}}\) Taking the power of \(\frac{1}{3}\) on both sides is not needed as we are looking for order and degree. Instead, we raise both sides to the power of 1.
  2. 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.
  3. The degree of a differential equation is the power of the highest order derivative, after the equation has been expressed in a form where all derivatives are free from radicals and fractions. The given equation is \([1+(\frac{dy}{dx})^{2}]^{3}=\frac{d^{2}y}{dx^{2}}\). The power of the highest order derivative \(\frac{d^{2}y}{dx^{2}}\) is 1. Therefore, the degree is 1.
  4. Thus, the order and degree of the given differential equation are 2 and 1, respectively.

Correct Answer: (C) 2, 1

AI Suggestion: Option C

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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 values from 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.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's knowledge of definitions and properties related to differential equations as covered in the textbook.

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