What is the general solution of the differential equation dydx=y−xy+x\frac{dy}{dx} = \frac{y-x}{y+x}dxdy=y+xy−x?
12ln(x2+y2)+arctan(yx)=C\frac{1}{2}\ln(x^2+y^2) + \arctan(\frac{y}{x}) = C21ln(x2+y2)+arctan(xy)=C
12ln(x2+y2)−arctan(yx)=C\frac{1}{2}\ln(x^2+y^2) - \arctan(\frac{y}{x}) = C21ln(x2+y2)−arctan(xy)=C
x2+y2=Cx^2+y^2 = Cx2+y2=C
ln(x2+y2)=C\ln(x^2+y^2) = Cln(x2+y2)=C