Question

The solution of $\frac{x^{3}dx + yx^{2}dy}{\sqrt{x^{2} + y^{2}}}$= ydx – xdy is:

• A. $\sqrt{x^{2} + y^{2}}$= Cx
• B. $\sqrt{x^{2} + y^{2}}$+ y/x = C
• C. $\sqrt{x^{2} + y^{2}}$+ y/x² = C
• D. (x² + y²)² + xy² = C

Answer 1

Answer: (B)

$\sqrt{x^{2} + y^{2}}$+ y/x = C

Answer 2

$\frac{x^{2}(xdx + ydy)}{\sqrt{x^{2} + y^{2}}}$= ydx –x dy

Or $\int_{}^{}{\frac{1}{2}\frac{d(x^{2} + y^{2})}{\sqrt{x^{2} + y^{2}}}}$= $\int_{}^{}\frac{ydx - xdy}{x^{2}}$

Ž $\frac{1}{2}$2. $\sqrt{x^{2} + y^{2}}$= –$\frac{y}{x}$+ C