CBSE Class 12 Mathematics 2026 Main Paper 65/5/3 · Q283 Markslinear_differential_equations
CBSE Class 12 Mathematics 2026 Main Paper 65/5/3 · Question 28 (Differential Equations)
Solve (x−sin y)dy+tan y dx=0.
✅ Step-by-Step Solution
Final Answer: x sin y=(sin² y)/2+C, with tan y defined. Constant branches y=nπ also satisfy the original equation.
- On intervals with sin y and cos y nonzero, write dx/dy+x cot y=cos y.
- Multiply by sin y to obtain d(x sin y)/dy=sin y cos y.
- Integrating gives x sin y=(sin² y)/2+C. For constant y=nπ the original differential form vanishes.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] On intervals with sin y and cos y nonzero, write dx/dy+x cot y=cos y.
- [2 marks] Multiply by sin y to obtain d(x sin y)/dy=sin y cos y.
- [0.5 marks] Integrating gives x sin y=(sin² y)/2+C. For constant y=nπ the original differential form vanishes.
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