Xdx + ydy = xdx + ydy/(x2 + y2)

1.	Xdx + ydy = xdx + ydy/(x2 + y2)
Answer» 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)] \(=\frac{2x\,dx+2y\,dy}{x^2+y^2})\)

Answer»

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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Xdx + ydy = xdx + ydy/(x2 + y2)

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