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in Differentiation by (15 points)
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Xdx + ydy = xdx + ydy/(x+ y2)

by (15 points)
Can u give me solution to this problem

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1 Answer

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x dx + y dy \(=\frac{x\,dx+y\,dy}{x^2+y^2}\)

⇒ 2x dx + 2y dy \(=\frac{2x\,dx+2y\,dy}{x^2+y^2}\) (Multiply both sides by 2)

⇒ ∫2x dx + ∫2y dy \(=\int\frac{2x\,dx+2y\,dy}{x^2+y^2}\)

⇒ x2 + y2 = ln(x2 + y2) + c (∵ d[ln(x2+y2)] \(=\frac{2x\,dx+2y\,dy}{x^2+y^2})\)

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