Determine the general solution for dydx=y2+x2xy\frac{dy}{dx} = \frac{y^2+x^2}{xy}dxdy=xyy2+x2 using the substitution v=y/xv = y/xv=y/x.
y2=x2(ln(x2)+C)y^2 = x^2(\ln(x^2) + C)y2=x2(ln(x2)+C)
y2=x2(2ln∣x∣+C)y^2 = x^2(2\ln|x| + C)y2=x2(2ln∣x∣+C)
y=x(lnx+C)y = x(\ln x + C)y=x(lnx+C)
y2=2x2+Cy^2 = 2x^2 + Cy2=2x2+C