The order of a differential equation is the highest order derivative present in the equation.
However, the order is defined only when the differential equation is a polynomial equation in derivatives.
In the given equation, \(\frac{d^{4}y}{dx^{4}}-sin(\frac{d^{2}y}{dx^{2}})=5\), the term \(sin(\frac{d^{2}y}{dx^{2}})\) is a non-polynomial function of the derivative \(\frac{d^{2}y}{dx^{2}}\).
Therefore, the order of the differential equation is not defined.
Correct Answer: not defined
AI Suggestion: Option D
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Pedagogical Audit
Bloom's Analysis:
This is an ANALYZE question because the student needs to analyze the given differential equation to determine its order, considering the presence of a non-polynomial function of a derivative.
Knowledge Dimension:CONCEPTUAL
Justification:The question requires understanding the concept of the order of a differential equation and recognizing when it is not defined due to the presence of a non-polynomial function of a derivative.
Syllabus Audit:
In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the understanding of the definition of the order of a differential equation, a concept covered in the textbook.