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GUJCET · Maths · Differential Equations
The integrating factor of the differential equation \(\left(\tan ^{-1} y-x\right) d y=\left(1+y^2\right) d x\) is ____________ .
- A \(e^{\tan ^{-1} x}\)
- B \(e^{1+y^2}\)
- C \(e^y\)
- D \(e^{\tan ^{-1} y}\)
Answer & Solution
Correct Answer
(D) \(e^{\tan ^{-1} y}\)
Step-by-step Solution
Detailed explanation
\(\left(\tan ^{-1} y-x\right) d y=\left(1+y^2\right) d x\) \(\frac{dx}{dy} + \frac{x}{1+y^2} = \frac{\tan^{-1} y}{1+y^2}\)
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