Class 12 Differential Equations · Short Answer2 Marksorder_and_degree
Class 12 Maths · Differential Equations · Short Answer #43
Find the sum of order and degree of (x + y′)² = (y′)² + 1.
✅ Step-by-Step Solution
Final Answer: 2
- Expand: x² + 2xy′ + (y′)² = (y′)² + 1.
- Cancel the identical squared-derivative terms: 2xy′ + x² − 1 = 0. The reduced differential polynomial has order 1 and degree 1.
- The required sum is 1 + 1 = 2.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Expand: x² + 2xy′ + (y′)² = (y′)² + 1.
- [1 mark] Cancel the identical squared-derivative terms: 2xy′ + x² − 1 = 0. The reduced differential polynomial has order 1 and degree 1.
- [0.5 marks] The required sum is 1 + 1 = 2.
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