Class 12 Differential Equations · Short Answer2 Marksfirst_order_differential_equations
Class 12 Maths · Differential Equations · Short Answer #41
Solve cos x · y′ = cos 3x − cos 2x.
✅ Step-by-Step Solution
Final Answer: y = sin 2x − x − 2sin x + ln|sec x + tan x| + C, cos x ≠ 0.
- Divide by cos x and use cos 3x = 4cos³x − 3cos x and cos 2x = 2cos²x − 1.
- Then y′ = 4cos²x − 3 − 2cos x + sec x = 2cos 2x − 1 − 2cos x + sec x. Integrate each term.
- Thus y = sin 2x − x − 2sin x + ln|sec x + tan x| + C on a connected interval cos x ≠ 0.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Divide by cos x and use cos 3x = 4cos³x − 3cos x and cos 2x = 2cos²x − 1.
- [1 mark] Then y′ = 4cos²x − 3 − 2cos x + sec x = 2cos 2x − 1 − 2cos x + sec x. Integrate each term.
- [0.5 marks] Thus y = sin 2x − x − 2sin x + ln|sec x + tan x| + C on a connected interval cos x ≠ 0.
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