Class 12 Differential Equations · Long Answer3 Markslinear_differential_equations
Class 12 Maths · Differential Equations · Long Answer #96
Solve cos²x · y′ + y = tan x.
✅ Step-by-Step Solution
Final Answer: y = tan x − 1 + Ce^(−tan x), cos x ≠ 0.
- Divide by cos²x to obtain y′ + sec²x y = tan x sec²x; IF = e^(tan x).
- Then ye^(tan x) = ∫tan x sec²x e^(tan x)dx + C.
- With t = tan x, ∫teᵗdt = (t − 1)eᵗ.
- Thus y = tan x − 1 + Ce^(−tan x), on any connected interval cos x ≠ 0.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Divide by cos²x to obtain y′ + sec²x y = tan x sec²x; IF = e^(tan x).
- [1 mark] Then ye^(tan x) = ∫tan x sec²x e^(tan x)dx + C.
- [1 mark] With t = tan x, ∫teᵗdt = (t − 1)eᵗ.
- [0.5 marks] Thus y = tan x − 1 + Ce^(−tan x), on any connected interval cos x ≠ 0.
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