NCERT Class 12 · Ch 9 Exercise 9.5 · Q18
NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.5 Question 18
Find an integrating factor of xy′−y=2x².
💡 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: 1/x.
- For x≠0 write y′−y/x=2x. Thus P=−1/x.
- μ=e^(∫Pdx)=e^(−log|x|), equivalent up to a nonzero constant to 1/x on either sign interval.
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