Identify the Order: The order of a differential equation is the highest order derivative present in the equation. In the given equation, \(-\frac{d^{4}y}{dx^{4}}+2e^{dy/dx}+y^{2}=0\), the highest order derivative is \(\frac{d^{4}y}{dx^{4}}\), which is the fourth derivative. Therefore, the order is 4.
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, the term \(e^{dy/dx}\) is present. This term makes the equation non-polynomial in derivatives because \(e^x\) has an infinite series expansion. Therefore, the degree of the differential equation is not defined.
Conclusion: The order is 4, and the degree is not defined.
Correct Answer: (B) 4, not defined
AI Suggestion: Option B
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Pedagogical Audit
Bloom's Analysis:
This is an APPLY question because it requires students to apply their knowledge of differential equations, specifically the definitions of order and degree, to a given equation.
Knowledge Dimension:CONCEPTUAL
Justification:The question tests the understanding of 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 assesses the understanding of definitions and concepts related to differential equations as covered in the textbook.