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CBSE Class 12 Mathematics 2026 Supplementary Paper 65(B)/7 · Q81 Marksintegrating_factor

CBSE Class 12 Mathematics 2026 Supplementary Paper 65(B)/7 · Question 8 (Differential Equations)

Find the integrating factor for x dy+(2y−x³)dx=0 on x≠0.

(A) x
(B) 1/x
(C) x²
(D) 1/x²

✅ Step-by-Step Solution

Final Answer: x²

Divide by x to get y′+2y/x=x², whose integrating factor is exp(2 ln|x|)=x².

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