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Find the equation of the curve that passes through the point \((a,-1/a)\) and satisfies the differential equation \[ y - x\frac{dy}{dx} = a\left(y^2 + \frac{dy}{dx}\right). \]
- \((x + a)(1 + ay) = -4a^2y\)
- \((x + a)(1 - ay) = 4a^2y\)
- \((c + a)(1 - ay) = -4a^2y\)
- None of these
Correct answer: \((x + a)(1 - ay) = 4a^2y\)
Solution
The correct option is right because it satisfies both the given differential equation and the condition of passing through the specified point, confirming that it is a valid solution for the curve.
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