CUET · MATHS · PYQ PAPER 2025
The integrating factor of the differential equation \(\frac{d y}{d x}=x+x y\) is:
- A \(e^{-\frac{x}{2}}\)
- B \(e^{-\frac{x^2}{2}}\)
- C \(e^{\frac{x^2}{2}}\)
- D \(e^{\frac{x}{2}}\)
Answer & Solution
Correct Answer
(B) \(e^{-\frac{x^2}{2}}\)
Step-by-step Solution
Detailed explanation
Rearrange: \(\frac{d y}{d x} - xy = x\) \(P(x) = -x\) IF = \(e^{\int -x dx}\) IF = \(e^{-\frac{x^2}{2}}\)
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