Determine the integrating factor μ(x)\mu(x)μ(x) for (3xy+y2)dx+(x2+xy)dy=0(3xy + y^2)dx + (x^2 + xy)dy = 0(3xy+y2)dx+(x2+xy)dy=0 assuming μ=μ(x)\mu = \mu(x)μ=μ(x).
μ(x)=x\mu(x) = xμ(x)=x
μ(x)=x2\mu(x) = x^2μ(x)=x2
μ(x)=x−1\mu(x) = x^{-1}μ(x)=x−1
μ(x)=ln∣x∣\mu(x) = \ln|x|μ(x)=ln∣x∣