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Long Division Method to Divide Two Polynomials

Solve :- xy...

Question

Solve :- $x y (y + 10) d y = (x^{2} + 1) d x$

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Solution

$(y^{2} + 10 y) d y = (x + \frac{1}{x}) d x$
$\int (y^{2} + 10 y) d y = \int (x + \frac{1}{x}) d x$
$⟹ \frac{y^{3}}{3} + 5 y^{2} = \frac{x^{2}}{2} + ln | x | + C$

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