Class 12 Differential Equations · Conceptual Answer1 Markslinear_differential_equations
Class 12 Maths · Differential Equations · Conceptual Answer #33
Solve (y + 3x²)dx/dy = x.
✅ Step-by-Step Solution
Final Answer: y = 3x² + Cx, locally inverted where dy/dx = 6x + C ≠ 0; also x(y) = 0.
- For x ≠ 0, write dy/dx − y/x = 3x. Then (y/x)′ = 3, giving y/x = 3x + C. The original x(y) equation also admits x = 0.
- y = 3x² + Cx, locally inverted where dy/dx = 6x + C ≠ 0; also x(y) = 0.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] For x ≠ 0, write dy/dx − y/x = 3x. Then (y/x)′ = 3, giving y/x = 3x + C. The original x(y) equation also admits x = 0.
- [0.5 marks] y = 3x² + Cx, locally inverted where dy/dx = 6x + C ≠ 0; also x(y) = 0.
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