Class 12 Differential Equations · Short Answer2 Marksseparable_differential_equations
Class 12 Maths · Differential Equations · Short Answer #38
Solve y′ = y tan x with y(0) = 1.
✅ Step-by-Step Solution
Final Answer: y = sec x, −π/2 < x < π/2.
- Separate dy/y = tan x dx near the nonzero initial value.
- Integrate ln|y| = −ln|cos x| + C, hence y cos x = C₁. At x = 0, C₁ = 1.
- Thus y = sec x on the maximal interval (−π/2, π/2) containing 0.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Separate dy/y = tan x dx near the nonzero initial value.
- [1 mark] Integrate ln|y| = −ln|cos x| + C, hence y cos x = C₁. At x = 0, C₁ = 1.
- [0.5 marks] Thus y = sec x on the maximal interval (−π/2, π/2) containing 0.
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