Class 12 Differential Equations · Long Answer3 Markslinear_differential_equations
Class 12 Maths · Differential Equations · Long Answer #101
Solve y′ + y cot x = 2cos x, y(π/2) = 0.
✅ Step-by-Step Solution
Final Answer: y = −cos²x/sin x, 0 < x < π.
- IF = sin x on (0, π), so (y sin x)′ = 2sin x cos x.
- Integrate y sin x = sin²x + C.
- At x = π/2 and y = 0, C = −1.
- Thus y = (sin²x − 1)/sin x = −cos²x/sin x, 0 < x < π.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] IF = sin x on (0, π), so (y sin x)′ = 2sin x cos x.
- [1 mark] Integrate y sin x = sin²x + C.
- [1 mark] At x = π/2 and y = 0, C = −1.
- [0.5 marks] Thus y = (sin²x − 1)/sin x = −cos²x/sin x, 0 < x < π.
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