NCERT Class 12 · Ch 9 Miscellaneous Exercise · Q13
NCERT Class 12 Maths · Chapter 9 Differential Equations · Miscellaneous Exercise Question 13
Choose the general solution of (y dx−x dy)/y=0.
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: C: y=Cx (on the original domain y≠0).
- The equation is y−xy′=0, so y′/y=1/x on nonzero-x branches.
- Integrating gives log|y|=log|x|+K, equivalently y=Cx. Keep the original exclusion y=0 where the written quotient is undefined.
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