Class 12 Differential Equations · Long Answer3 Markslinear_differential_equations
Class 12 Maths · Differential Equations · Long Answer #104
Solve (1 + x²)dy + 2xy dx = cot x dx.
✅ Step-by-Step Solution
Final Answer: y = [ln|sin x| + C]/(1 + x²), sin x ≠ 0.
- Write y′ + 2xy/(1 + x²) = cot x/(1 + x²).
- IF = 1 + x², so [(1 + x²)y]′ = cot x.
- Integrate (1 + x²)y = ln|sin x| + C.
- Thus y = [ln|sin x| + C]/(1 + x²), on any connected interval sin x ≠ 0.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Write y′ + 2xy/(1 + x²) = cot x/(1 + x²).
- [1 mark] IF = 1 + x², so [(1 + x²)y]′ = cot x.
- [1 mark] Integrate (1 + x²)y = ln|sin x| + C.
- [0.5 marks] Thus y = [ln|sin x| + C]/(1 + x²), on any connected interval sin x ≠ 0.
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