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Exercise 6.2 · Q17

Q.Obtain the differential equation by eliminating the arbitrary constant: y=a+axy=a+\dfrac{a}{x}

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Differentiate y=a+axy=a+\dfrac{a}{x} w.r.t. xx: dydx=−ax2\dfrac{dy}{dx}=-\dfrac{a}{x^2}, so a=−x2dydxa=-x^2\dfrac{dy}{dx}. Substitute back into y=a(1+1x)y=a\left(1+\dfrac{1}{x}\right): $y=-x^2\dfrac{dy}{dx}\left(1+\dfrac{1}{x}\right)=-x^2\dfrac{dy}{dx}-x\dfrac …

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