Class 12 Differential Equations · Short Answer2 Marksintegrating_factors
Class 12 Maths · Differential Equations · Short Answer #93
Find an integrating factor of y′ + y = (1 + y)/x.
✅ Step-by-Step Solution
Final Answer: eˣ/x, x ≠ 0.
- Rearrange to y′ + (1 − 1/x)y = 1/x.
- Integrate P: ∫(1 − 1/x)dx = x − ln|x|. The positive IF is eˣ/|x|.
- A convenient proportional signed integrating factor is eˣ/x on each connected interval x ≠ 0.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Rearrange to y′ + (1 − 1/x)y = 1/x.
- [1 mark] Integrate P: ∫(1 − 1/x)dx = x − ln|x|. The positive IF is eˣ/|x|.
- [0.5 marks] A convenient proportional signed integrating factor is eˣ/x on each connected interval x ≠ 0.
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