NCERT Class 12 · Ch 9 Exercise 9.3 · Q7
NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.3 Question 7
Solve y log y dx−x dy=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: y=e^(Cx), including y=1.
- The real equation requires y>0, with x≠0 when solved for y′. Put z=log y so z′=z/x.
- Integrate z′/z=1/x for z≠0, obtaining z=Cx. The zero solution z=0 is included by C=0.
- Thus y=e^(Cx), including y=1.
- Differentiate the resulting relation to recover the equation on intervals where the original expressions and the required slope are defined.
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All Questions in Differential Equations — Exercise 9.3
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