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Mathematics · JEE | DIFFERENTIAL EQUATIONS
हिन्दीWhat is the integrating factor for the linear differential equation \( (1 - y^2) \frac{dx}{dy} + yx = ay \) for \( -1 < y < 1 \)?
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Correct answer · Option B
\( \frac{1}{\sqrt{1 - y^2}} \)
Explanation
Dividing by \( 1-y^2 \), \( P_1 = \frac{y}{1-y^2} \). I.F. = \( e^{\int \frac{y}{1-y^2}dy} = e^{-\frac{1}{2}\ln(1-y^2)} = \frac{1}{\sqrt{1-y^2}} \).
