Class CBSE Class 12 Mathematics Differential Equations Q #654
KNOWLEDGE BASED
APPLY
1 Marks 2025 AISSCE(Board Exam) MCQ SINGLE
The sum of the order and degree of the differential equation \([1+(\frac{dy}{dx})^{2}]^{3}=\frac{d^{2}y}{dx^{2}}\) is:
(A) 2
(B) \(\frac{5}{2}\)
(C) 3
(D) 4
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Correct Answer: C

AI Tutor Explanation

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Step-by-Step Solution

  1. First, rewrite the given differential equation to determine its order and degree. The equation is \([1+(\frac{dy}{dx})^{2}]^{3}=\frac{d^{2}y}{dx^{2}}\). To find the degree, we need to express the equation in a polynomial form.
  2. The equation can be written as \([1+(\frac{dy}{dx})^{2}]^{3/2}=\frac{d^{2}y}{dx^{2}}\). Squaring both sides, we get \([1+(\frac{dy}{dx})^{2}]^{3}=(\frac{d^{2}y}{dx^{2}})^{2}\).
  3. The order of a differential equation is the highest order derivative present in the equation. Here, the highest order derivative is \(\frac{d^{2}y}{dx^{2}}\), which is of order 2.
  4. The degree of a differential equation is the power of the highest order derivative, when the equation is expressed in a polynomial form. Here, the power of \(\frac{d^{2}y}{dx^{2}}\) is 2.
  5. The sum of the order and degree is 2 + 2 = 4.

Correct Answer: 4

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 knowledge of differential equations, specifically how to determine the order and degree, to solve the given problem.
Knowledge Dimension: CONCEPTUAL
Justification: The question requires understanding the concepts of order and degree of a differential equation and applying them to a specific equation.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's understanding of definitions and procedures related to differential equations as covered in the textbook.

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