CBSE Class 12 Mathematics 2026 Main Paper 65/5/1 · Q283 Markslinear_differential_equations
CBSE Class 12 Mathematics 2026 Main Paper 65/5/1 · Question 28 (Differential Equations)
Solve (x+2y³)dy=y dx.
✅ Step-by-Step Solution
Final Answer: x=y³+Cy on y≠0 branches; y=0 also satisfies the differential equation.
- Treat x as a function of y for y≠0. Then dx/dy−x/y=2y².
- Divide by y to recognize d(x/y)/dy=2y.
- Integrate and multiply through by y. The constant solution y=0 satisfies the original form directly.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Treat x as a function of y for y≠0. Then dx/dy−x/y=2y².
- [2 marks] Divide by y to recognize d(x/y)/dy=2y.
- [0.5 marks] Integrate and multiply through by y. The constant solution y=0 satisfies the original form directly.
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