Class 12 Differential Equations · Short Answer2 Marksintegrating_factors
Class 12 Maths · Differential Equations · Short Answer #37
Find an integrating factor after writing (1 + y²) + (2xy − cot y)y′ = 0 as a linear equation for x(y).
✅ Step-by-Step Solution
Final Answer: 1 + y², on intervals sin y ≠ 0.
- Write dx/dy + [2y/(1 + y²)]x = cot y/(1 + y²).
- Integrate P: ∫2y/(1 + y²)dy = ln(1 + y²).
- The integrating factor is exp(ln(1 + y²)) = 1 + y²; cot y requires sin y ≠ 0.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Write dx/dy + [2y/(1 + y²)]x = cot y/(1 + y²).
- [1 mark] Integrate P: ∫2y/(1 + y²)dy = ln(1 + y²).
- [0.5 marks] The integrating factor is exp(ln(1 + y²)) = 1 + y²; cot y requires sin y ≠ 0.
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