Class 12 Differential Equations · Short Answer2 Markslinear_differential_equations
Class 12 Maths · Differential Equations · Short Answer #36
Solve (y + 3x²)dx/dy = x.
✅ Step-by-Step Solution
Final Answer: y = 3x² + Cx, locally inverted where 6x + C ≠ 0; also x(y) = 0.
- For x ≠ 0, rewrite as dy/dx − y/x = 3x; IF = 1/x.
- Then (y/x)′ = 3, so y/x = 3x + C. The original equation separately admits x(y) = 0.
- Therefore y = 3x² + Cx describes the nonzero branches wherever locally invertible (6x + C ≠ 0); include x(y) = 0.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] For x ≠ 0, rewrite as dy/dx − y/x = 3x; IF = 1/x.
- [1 mark] Then (y/x)′ = 3, so y/x = 3x + C. The original equation separately admits x(y) = 0.
- [0.5 marks] Therefore y = 3x² + Cx describes the nonzero branches wherever locally invertible (6x + C ≠ 0); include x(y) = 0.
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