Question

The solution curve of the differential equation,]

(xdx + ydy) $\sqrt{x^{2} + y^{2}}$= (xdy – ydx) $\sqrt{1 - x^{2} - y^{2}}$ are –

• A. Circles of radius 1 through the origin
• B. Circles of radius 1/2 through the origin
• C. Circles not through the origin
• D. Not the circles

Answer 1

Answer: (B)

Circles of radius 1/2 through the origin

Answer 2

x = r cosq, y = sinq, $\frac{dr}{| - r^{2}|}$ = dq ® sin^–1r + q + a

Ž r = sin(q + f)

r² = ycosa + xsina

x² + y² – xsina – ycosa = 0

\ radius = ½