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Question: The general solution of the differential equation (*x* + *y*)*dx* + *xdy* = 0 is...

The general solution of the differential equation (x + y)dx + xdy = 0 is

A

x2+y2=cx^{2} + y^{2} = c

B

2x2−y2=c2x^{2} - y^{2} = c

C

x2+2xy=cx^{2} + 2xy = c

D

y2+2xy=cy^{2} + 2xy = c

Answer

x2+2xy=cx^{2} + 2xy = c

Explanation

Solution

We have xdx + (ydx + xdy) = 0 ⇒ xdx + d(xy) = 0

Integrating, x22+xy=c2\frac{x^{2}}{2} + xy = \frac{c}{2}

∴ x2+2xy=cx^{2} + 2xy = c