NCERT Class 12 · Ch 9 Miscellaneous Exercise · Q14
NCERT Class 12 Maths · Chapter 9 Differential Equations · Miscellaneous Exercise Question 14
Choose the general solution of dx/dy+P₁(y)x=Q₁(y).
💡 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: x e^(∫P₁dy)=∫[Q₁e^(∫P₁dy)]dy+C.
- Here y is the independent variable. The integrating factor is μ(y)=e^(∫P₁dy).
- Multiplication gives d(μx)/dy=μQ₁. Integrate in y to obtain option C.
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