CUET · MATHS · PYQ PAPER 2023
Integrating factor of the differential equation \(x \frac{d y}{d x}-y=3 x^2\) is:
- A \(-x\)
- B \(\frac{1}{x}\)
- C \(-\log x\)
- D \(e^{-\infty}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{x}\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x} - \frac{1}{x}y = 3x\) \(P(x) = -\frac{1}{x}\) \(IF = e^{\int P(x) dx} = e^{\int -\frac{1}{x} dx} = e^{-\ln x} = e^{\ln x^{-1}} = \frac{1}{x}\)
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